2021
20
1
0
370
Kernel Ridge Estimator for the Partially Linear Model under Right-Censored Data
2
2
Objective: This paper aims to introduce a modified kernel-type ridge estimator for partially linear models under randomly-right censored data. Such models include two main issues that need to be solved: multi-collinearity and censorship. To address these issues, we improved the kernel estimator based on synthetic data transformation and kNN imputation techniques. The key idea of this paper is to obtain a satisfactory estimate of the partially linear model with multi-collinear and right-censored using a modified ridge estimator. Results: To determine the performance of the method, a detailed simulation study is carried out and a kernel-type ridge estimator for PLM is investigated for two censorship solution techniques. The results are compared and presented with tables and figures. Necessary derivations for the modified semiparametric estimator are given in appendices.
1
26
Syed Ejaz
Ahmed
Syed Ejaz
Ahmed
Brock University, Faculty of Mathematics and Science, Department of Mathematics and Statistics, Niagara Region, 1812 Sir Isaac Brock Way, St. Catharines, ON, L2S 3A1, Canada
sahmed5@brocku.ca
Dursun
Aydın
Dursun
Aydın
Mugla Sitki Kocman University, Faculty of Science, Department of Statistics, 48000, Mugla, Turkey
duaydin@hotmail.com
Ersin
Yılmaz
Ersin
Yılmaz
Mugla Sitki Kocman University, Faculty of Science, Department of Statistics, 48000, Mugla, Turkey
yilmazersin13@hotmail.com
Kernel Smoothing
KNN Imputation
Multi-Collinear Data
Partially Linear Model
Ridge Type Estimator
Right-Censored Data.
[Ahmed, S. E., Aydın, D., and Yılmaz, E. (2020), Nonparametric regression estimates based on imputation techniques for right-censored data. Proceedings of the Thirteenth International Conference on Management Science and Engineering Management, ICMSEM 2019, Advances in Intelligent Systems and Computing, Vol 1001, Springer, Cham.##Ahmed, S. E. (2014), Penalty, Shrinkage and Pretest Strategies: Variable Selection and Estimation. Springer, New York, https://www.springer.com/gp/book/9783319031484.##Batista, G., and Monard, M. (2002), An analysis of four missing data treatment methods for supervised learning, Applied Artificial Intelligence, 17, 519-533.##Hoerl, A. E., and Kennard, R. W. (1970), Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.##Kaplan, E. L., and Meier, P. (1958), Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457-481.##Koul, H., Susarla, V., and Van Ryzin, J. (1981), Regression analysis with randomly right censored data. The Annals of Statistics, 9, 1276-88.##Liang, H. (2006), Estimation in partially linear models and numerical comparisons. Computational Statistics and Data Analysis, 50(3), 675-685.##Liang, H., and Zhou, Y. (2008), Semiparametric Inference for ROC curves with censoring. Scandinavian Journal of Statistics, 35(2), 212-227.##Miller, R. G. (1976), Least squares regression with censored data. Biometrika, 63, 449-64.##Orbe, J., Ferreira, E., and Nunez-Anton, V. (2003), Censored Partial Regression. Biostatistics, 4(1), 109-121.##Ruppert, D., Wand, M. P., and Carroll, R. J. (2003), Semiparametric regression. Cambridge University Press, New York.##Schimek, M. G. (2000), Smoothing and Regression: Approaches, Computation and Application. John Wiley & Sons, Hoboken, NJ.##Shim, J. Y. (2005), Censored kernel ridge regression. Journal of the Korean Data and Information Science Society, 16(4), 1045-1052.##Stute, W. (1993), Consistent Estimation Under Random Censorship When Covariables Are Present. Journal Of Multivariate Analysis, 4, 89-103.##Yenduri, S., and Iyengar S. S. (2007), Performance evaluation of imputation methods for incomplete datasets. International Journal of Software Engineering and Knowledge Engineering, 17, 127-152.##Yüzbaşı, B., Arashi, M., and Ahmed, S. E. (2017), Shrinkage estimation strategies in generalized ridge regression models under low/high-dimension regime. International Statistical Review, 88(1), 229-251.## ##]
Variants of Mixtures: Information Properties and Applications
2
2
In recent years, we have studied information properties of various types of mixtures of probability distributions and introduced a new type, which includes previously known mixtures as special cases. These studies are disseminated in different fields: reliability engineering, econometrics, operations research, probability, the information theory, and data mining. This paper presents a holistic view of these studies and provides further insights and examples. We note that the insightful probabilistic formulation of the mixing parameters stipulated by Behboodian (1972) is required for a representation of the well-known information measure of the arithmetic mixture. Applications of this information measure presented in this paper include lifetime modeling, system reliability, measuring uncertainty and disagreement of forecasters, probability modeling with partial information, and information loss of kernel estimation. Probabilistic formulations of the mixing weights for various types of mixtures provide the Bayes-Fisher information and the Bayes risk of the mean residual function.
27
59
Omid
Ardakani
Omid
Ardakani
Department of Economics, Georgia Southern University, Savannah, Georgia, USA
oardakani@georgiasouthern.edu
Majid
Asadi
Majid
Asadi
Department of Statistics, University of Isfahan, Isfahan, Iran
m.asadi@sci.ui.ac.ir
Nader
Ebrahimi
Nader
Ebrahimi
Department of Statistics, Northern Illinois University, DeKalb, Illinois, USA
nebrahim@niu.edu
Ehsan
Soofi
Ehsan
Soofi
Lubar School of Business, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA
esoofi@uwm.edu
Arithmetic Mixture
Geometric Mixture
Jensen-Shannon
Kullback-Leibler.
[Ardakani, O. M., Ebrahimi, N., and Soofi, E. S. (2018), Ranking forecasts by stochastic error distance, information and reliability measures. International Statistical Review, 86(3), 442-468.##Ardakani, O. M., Asadi, M., Ebrahimi, N., and Soofi, E. S. (2020), MR plot: A big data tool for distinguishing distributions. Statistical Analysis and Data Mining the ASA Data Science Journal, 13, 405-418.##Asadi, M. and Zohrevand, Y. (2007), On the dynamic cumulative residual entropy. Journal of Statistical Planning and Inference, 137, 1931-1941.##Asadi, M., Ebrahimi, N., and Soofi, E. S. (2017), Connections of Gini, Fisher, and Shannon, by Bayes risk under proportional hazards. Journal of Applied Probability, 54, 1027-1050.##Asadi, M., Ebrahimi, N., and Soofi, E. S. (2018), Optimal hazard models based on partial information. European Journal of Operational Research, 270(2), 1-11.##Asadi, M., Ebrahimi, N., and Soofi, E. S. (2019), The alpha-mixture of survival functions. Journal of Applied Probability, 56(4), 1151-1167.##Asadi, M., Ebrahimi, N., kharazmi, O., and Soofi, E. S. (2019), Mixture models, Bayes Fisher information, and divergence measures. IEEE Transactions on Information Theory, 65, 2316-2321.##Asadi, M., Ebrahimi, N., Soofi, E. S., and Zohrevand, Y. (2016), Jensen-Shannon information of the coherent system lifetime. Reliability Engineering and System Safety, 156(C), 244-255.##Bajgiran, A. H., Mardikoraem, M., and Soofi, E. S. (2021), Maximum entropy distributions with quantile information. European Journal of Operational Research, 290(1), 196-209.##Barlow, R. E., Marshall, A. W., and Proschan, F. (1963), Properties of probability distributions with monotone hazard rate. Annals of Mathematical Statistics, 34, 375-389.##Behboodian, J. (1970), On a mixture of normal distributions. Biometrika, 57(1), 215-217.##Behboodian, J. (1972), On the distribution of a symmetric statistics from a mixed population. Technometrics, 14, 919-923.##Beheshti, N., Racine, J. S., and Soofi, E. S. (2019), Information measures of kernel estimation. Econometric Reviews, 38(1), 47-68.##Bercher, J. F. (2011), Escort entropies and divergences and related canonical distribution. Physics Letters A, 375, 2969-2973.##Bercher, J. F. (2012), A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians. Physica a: Statistical Mechanics and Its Applications, 391(19), 4460-4469.##Bissiri, P. G., Holmes, C. C., and Walker, S. G. (2016), A general framework for updating belief distributions. Journal of the Royal Statistical Society Series B, 78(5), 1103-1130.##Block, H. W., and Savits, T. H. (1997). Burn-in. Statistical Science, 12, 1-19.##Chernoff, H. (1952), A measure of asymptotic efficiency of tests of a hypothesis based on the sum of observations. Annals of Mathematical Statistics, 23 ,493-507.##Cover, T. M. and Thomas, J. A. (2006), Elements of Information Theory, 2nd ed.. New York: Wiley.##Harremoes, P. (2001), Binomial and Poisson distributions as maximum entropy distributions. IEEE Transactions on Information Theory, 47, 2039-2041.##Holmes, C. C., and Walker, S. G. (2017). Assigning a value to a power likelihood in a general Bayesian model. Biometrika, 104, 497-503.##Ibrahim, J. G., and Chen, M. H. (2000), Power prior distributions for regression models. Statistical Science, 15, 46-60.##Ibrahim, J. G., Chen, M. H., and Sinha, D. (2003), On optimality of the power prior. Journal of the American Statistical Association, 98, 204-213.##Kochar, S., Mukerjee, H., and Samaniego, F. J. (1999), The "signature" of a coherent system and its application to comparisons among systems. Naval Research Logistics, 46(5), 507-523.##https://doi.org/10.1002/(SICI)1520-6750(199908)46:5<507::AID-NAV4>3.0.CO;2-D##Kullback, S. (1959), Information theory and statistics. New York: Wiley (reprinted in 1968 by Dover).##Li, Q., and Racine (2007). Nonparametric Econometrics: Theory and Practice. New Jersey: Princeton University Press.##Lin, J. (1991), Divergence measures based on the Shannon entropy. Transactions on Information Theory, 37, 145-151.##Lindley, D. V. (1956), On a measure of the information provided by an experiment. Annals of Mathematical Statistics, 27, 986-1005.##Lynn, N. J., and Singpurwalla, N. D. (1997), Comment: "Burn-in'" makes us feel good. Statistical Science, 12, 13-19.##McCulloch, R. E. (1989), Local model influence. Journal of the American Statistical Association, 84, 473-478.##Mcvinish, M., Rousseau, J., and Mengersen, K. (2009), Bayesian goodness of fit testing with mixtures of triangular distributions. Scand. J Statist., 36, 337-354.##Navarro, J., and Rychlik, T. (2007), Reliability and expectation bounds for coherent systems with exchangeable components. Journal of Multivariate Analysis, 98(1), 102-113.##Rao, M., Chen, Y., Vemuri, B. C., and Wang, F. (2004), Cumulative residual entropy: A new measure of information. IEEE Transactions on Information Theory, 50, 1220-1228.##Samaniego, F. J. (1985), On closure of the IFR class under formation of coherent systems. IEEE Transactions on Reliability, R-34(1), 69-72.##Samaniego, F. J. (2007), System signatures and their applications in engineering reliability. Springer.##Shaked, M., and Shanthikumar, J. G. (2007), Stochastic orders. Springer.##Shaked, M., and Suarez-Llorens, A. (2003), On the comparison of reliability experiments based on the convolution order. Journal of the American Statistical Association, 98(463), 693-702.##Shoja, M., and Soofi, E. S. (2017), Uncertainty, information, and disagreement of economic forecasters. Econometric Reviews, 36(6-9), 796-817.##Soofi, E. S., Ebrahimi, N., and Habibullah, M. (1995), Information distinguishability with application to analysis of failure data. Journal of the American Statistical Association, 90, 657-668.##Tsallis, C. (1998), Generalized entropy-based criterion for consistent testing. Physics Review E, 58, 1442-1445.##Vakili-Nezhaad, G. R., and Mansoori, G. A. (2004), An application of non-extensive statistical mechanics to nanosystems. Journal of Computational and Theortical Nanonscience, 1, 233-235.##van Erven, T., and Harremo"es, P. (2014), R'enyi divergence and Kullback-Leibler divergence. IEEE Transactions on Information Theory, {bf 60, 3797-3820.##Walker, S. G. (2016), Bayesian information in an experiment and the Fisher information distance. Statistics and Probability Letters, {bf 112, 5-9.##Wang, W., and Lahiri, K. (2021), Estimating macroeconomic uncertainty and discord using info-metrics. In Innovations in info-metrics A cross-disciplinary perspective on information and information processing, 1-55.##Wang, L., and Madiman, M. (2014), Beyond the entropy power inequality, via rearrangements. IEEE Transactions on Information Theory, 60(9), 5116-5137.## ##]
Asymmetric Univariate and Bivariate Laplace and Generalized Laplace Distributions
2
2
Alternative specifications of univariate asymmetric Laplace models are described and investigated. A more general mixture model is then introduced. Bivariate extensions of these models are discussed in some detail, with particular emphasis on associated parameter estimation strategies. Multivariate versions of the models are briefly introduced.
61
81
Barry
Arnold
Barry
Arnold
Department of Statistics, University of California, Riverside, USA
barnold@ucr.edu
Matthew
Arvanitis
Matthew
Arvanitis
USDA Forest Products Laboratory, Madison, Wisconsin, USA
matthew.arvanitis@usda.gov
Asymmetric Laplace
Bivariate Laplace
Exponential Minima
Gamma Components
Generalized Asymmetric Laplace
Laplace
[Arnold, B.C. (2020), Some bivariate and multivariate models involving independent gamma distributed components. To appear in: Contributions to Statistical Distribution Theory and Inference, a Festschrift in Honor of C. R. Rao on the Occasion of His 100th Birthday.##Arnold, B. C., Ng, and H. K. T. (2011), Flexible bivariate beta distributions. Journal of Multivariate Analysis, 102, 1194-1202 .##Arvanitis, M. (2018), Likelihood-Free Estimation for Some Flexible Families of Distributions (Doctoral dissertation, UC Riverside).##Jones, M. C. (2019), On a characteristic property of distributions related to the Laplace. South African Statistical Journal, 53, 31-34.##Kozubowski, T. J., and Podgórski, K. (2000), A Multivariate and Asymmetric Generalization of Laplace Distribution. Computational Statistics, 15, 531-540.##Kozubowski, T. J., and Podgorski, K. (2000), Asymmetric Laplace distributions. Mathematical Scientist, 25(1), 37-46.## ##]
Ageing Orders of Series-Parallel and Parallel-Series Systems with Independent Subsystems Consisting of Dependent Components
2
2
In this paper, we consider series-parallel and parallel-series systems with independent subsystems consisting of dependent homogeneous components whose joint lifetimes are modeled by an Archimedean copula. Then, by considering two such systems with different numbers of components within each subsystem, we establish hazard rate and reversed hazard rate orderings between the two system lifetimes, and also discuss how these systems age relative to each other in terms of hazard rate and reversed hazard rate functions.
83
100
Narayanaswamy
Balakrishnan
Narayanaswamy
Balakrishnan
Department of Mathematics and Statistics, McMaster University, Hamilton, CANADA
bala@mcmaster.ca
Ghobad
Barmalzan
Ghobad
Barmalzan
Department of Statistics, University of Zabol, Sistan and Baluchestan, IRAN
ghbarmalzan@uoz.ac.ir
Ali Akbar
Hosseinzadeh
Ali Akbar
Hosseinzadeh
Department of Mathematics, University of Zabol, Sistan and Baluchestan, IRAN
hosseinzadeh@uoz.ac.ir
Relative Ageing Orders
Hazard Rate Order
Reversed Hazard Rate Order
Series-Parallel Systems
Parallel-Series Systems
Archimedean Copulas.
[Billionnet, A. (2008), Redundancy allocation for series-parallel systems using integer linear programming. IEEE Transactions on Reliability, 57, 507-516.##Coit, D. W., and Smith, A. E. (1996), Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Transactions on Reliability, 45, 254-260.##Ding, W., and Zhang, Y. (2018), Relative ageing of series and parallel systems: Effects of dependence and heterogeneity among components. Operations Research Letters, 46, 219-224.##El-Neweihi, E., Proschan, F., and Sethuraman, J. (1986), Optimal allocation of components in parallel-series and series-parallel systems. Journal of Applied Probability, 23, 770-777.##Fang, L., Balakrishnan, N., and Jin, Q. (2020), Optimal grouping of heterogeneous components in series-parallel and parallel-series systems under Archimedean copula dependence. Journal of Computational and Applied Mathematics, 377, 112916.##Kalashnikov, V. V., and Rachev, S. T. (1986), Characterization of queueing models and their stability. Theory and Mathematical Statistics, 2, 37-53.##Kotz, S., Balakrishnan, N., and Johnson, N. L. (2000), Continuous Multivariate Distributions. New York: John Wiley & Sons, 1(2)##Levitin, G., and Amari, S. V. (2009), Optimal load distribution in series-parallel systems. Reliability Engineering & System Safety, 94, 254-260.##Ling, X., Wei, Y., and Li, P. (2018), On optimal heterogeneous components grouping in series-parallel and parallel-series systems. Probability in the Engineering and Informational Sciences, 33, 564-578.##Muller, A., and Stoyan, D. (2002), Comparison Methods for Stochastic Models and Risks. Hoboken, New Jersey: John Wiley & Sons.##Nelsen, R. B. (2006), An Introduction to Copulas. New York: Springer.##Ramirez-Marquez, J. E., Coit, D. W., and Konak, A. (2004). Redundancy allocation for series-parallel systems using a max-min approach. IIE Transactions, 36, 891-898.##Rezaei, M., Gholizadeh, B., and Izadkhah, S. (2015). On relative reversed hazard rate order. Communications##in Statistics-Theory and Methods, 44, 300-308.##Sarhan, A .M., Al-Ruzaiza, A. S., Alwasel, I. A., and El-Gohary, A. I. (2004). Reliability equivalence of a series-parallel system. Applied Mathematics and Computation, 154, 257-277.##Shaked, M., and Shanthikumar, J. G. (2007) Stochastic Orders. New York: Springer.##Sun, M. X., Li, Y. F., and Zio, E. (2019). On the optimal redundancy allocation for multi-state series-parallel systems under epistemic uncertainty. Reliability Engineering & System Safety, 192, 106019.## ##]
On Burr III-Inverse Weibull Distribution with COVID-19 Applications
2
2
We introduce a flexible lifetime distribution called Burr III-Inverse Weibull (BIII-IW). The new proposed distribution has well-known sub-models. The BIII-IW density function includes exponential, left-skewed, right-skewed and symmetrical shapes. The BIII-IW model’s failure rate can be monotone and non-monotone depending on the parameter values. To show the importance of the BIII-IW distribution, we establish various mathematical properties such as random number generator, ordinary moments, conditional moments, residual life functions, reliability measures and characterizations. We address the maximum likelihood estimates (MLE) for the BIII-IW parameters and estimate the precision of the maximum likelihood estimators via a simulation study. We consider applications to two COVID-19 data sets to illustrate the potential of the BIII-IW model.
101
121
Fiaz Ahmad
Bhatti
Fiaz Ahmad
Bhatti
National College of Business Administration and Economics, Lahore, PAKISTAN
fiazahmad72@gmail.com
Sedigheh
Mirzaei Salehabadi
Sedigheh
Mirzaei Salehabadi
St. Jude Children’s Research Hospital, Memphis, TN, USA
Sedigheh.Mirzaei@stjude.org
Gholamhossein G
Hamedani
Gholamhossein G
Hamedani
Marquette University, Milwaukee, WI 53201-1881, USA
g.hamedani@mu.edu
Moment
Reliability
Characterizations
Maximum Likelihood Estimation.
[Abbas, S., Hameed, M., Cakmakyapan, S., and Malik, S. (2020), On gamma inverse Weibull distribution. Journal of the National Science Foundation of Sri Lanka, 47(4), 445-453.##Abbas, S., Taqi, S., Mustafa, F., Murtaza, M., and Shahbaz, M. (2017), Topp-Leone Inverse Weibull Distribution: Theory and Application.European Journal of Pure and Applied Mathematics, 10(5), 1005-1022.##Alzaatreh, A., Mansoory, M., Tahirz, M. H., Zubair, M., and Ghazalik, S. A. (2016), The gamma half-Cauchy distribution: Properties and applications. Hacettepe Journal of Mathematics and Statistics, 45(4), 1143-1159.##Alzaatreh, A., Lee, C., and Famoye, F. (2013), A new method for generating families of continuous distributions. Metron, 71(1), 63-79.##Bantan, R. A., Chesneau, C., Jamal, F., and Elgarhy, M. (2020), On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions. Mathematics, 8(6), 953.##Bhattacharyya, G. K., and Johnson, R. A. (1974), Estimation of reliability in a multicomponent stress-strength model. Journal of the American Statistical Association, 69(348), 966-970.##Elbatal, I., Condino, F., and Domma, F. (2016), Reflected generalized beta inverse Weibull distribution: definition and properties. Sankhya B, 78(2), 316-340.##Eliwa, M. S., El-Morshedy, M., and Ali, S. (2020), Exponentiated odd Chen-G family of distributions: statistical properties, Bayesian and non-Bayesian estimation with applications. Journal of Applied Statistics, 1-27.##Fayomi, A. (2019). The odd Frechet inverse Weibull distribution with application. Journal of Nonlinear Sciences and Applications, {bf 12, 165-172.##Glanzel W. A. (1987). Characterization theorem based on truncated moments and its application to some distribution families. Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, 75-84.##Hafida G. and Haitham Y. H. (2019), Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test. Journal of Applied Statistics, 47(3), 393-423.##Khan, M. S. (2010), The beta inverse Weibull distribution. International Transactions in Mathematical Sciences and Computer, 3(1), 113-119.##Khan, M. S., and King, R. (2016), New generalized inverse Weibull distribution for lifetime modeling. Communications for Statistical Applications and Methods, 23(2), 147-161.##Keller, A.Z. and Kamath, A.R.R. (1982), Alternative Reliability Models for Mechanical Systems. Proceeding of the 3rd International Conference on Reliability and Maintainability, 411-415.##Kotz S., Lai CD and Xie M. (2003), On the Effect of Redundancy for Systems with Dependent Components. IIE Transactions, 35(12), 1103-1110.##Eliwa M. S. , El-Morshedy M. and Ali S., (2020), Exponentiated odd Chen-G family of distributions: statistical properties, Bayesian and non-Bayesian estimation with applications. Journal of Applied Statistics.##Shahbaz, M. Q., Shahbaz, S., and Butt, N. S. (2012), The Kumaraswamy-Inverse Weibull Distribution. Pakistan Journal of Statistics and Operation Research, 8(3), 479-489.## ##]
Stage Life Testing with Missing Stage Information - an EM-Algorithm Approach
2
2
We consider a stage life testing model and assume that the information at which levels the failures occurred is not available. In order to find estimates for the lifetime distribution parameters, we propose an EM-algorithm approach which interprets the lack of knowledge about the stages as missing information. Furthermore, we illustrate the implementation difficulties caused by an increasing number of stages. The study is supplemented by a data example as well as simulations.
123
152
Erhard
Cramer
Erhard
Cramer
Institute of Statistics, RWTH Aachen University, D-52062 Aachen, GERMANY
erhard.cramer@rwth-aachen.de
Benjamin
Laumen
Benjamin
Laumen
Institute of Statistics, RWTH Aachen University, D-52062 Aachen, GERMANY
benjamin.laumen@rwth-aachen.de
EM-Algorithm
Exponential Distribution
Missing Information
Progressive Censoring
Stage Life Testing
Weibull Distribution
[Atkinson, K. E. (1989). An introduction to numerical analysis, John Wiley & Sons, Inc., 2nd edition.##Bairamov, I., and Eryilmaz, S. (2006). Spacings, exceedances and concomitants in progressive Type II censoring scheme. J. Statist. Plann. Inference, 136(3), 527-536.##Balakrishnan, N. (2009). A synthesis of exact inferential results for exponential step-stress models and associated optimal accelerated life-tests. Metrika, 69, 351-396.##Balakrishnan, N., and Aggarwala, R. (2000). Progressive censoring: theory, methods, and applications. Birkhauser, Boston.##Balakrishnan, N., and Cramer, E. (2014). The Art of Progressive Censoring: Applications to Reliability and Quality. Statistics for Industry and Technology. Birkhauser, New York.##Balakrishnan, N., and Cramer, E. (2021). Progressive censoring methodology: A review. In Pham, H., editor, Springer Handbook of Engineering Statistics, Springer, New York, 2. edition, to appear.##Balakrishnan, N., Han, D., and Iliopoulos, G. (2011). Exact inference for progressively Type-I censored exponential failure data. Metrika, 73(3), 335-358.##Balakrishnan, N., and Kateri, M. (2008). On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data.##Statistics & Probability Letters, 78(17), 2971-2975.##Cramer, E. (2017). Progressive Censoring Schemes. Inem Wiley StatsRef: Statistics Reference Online, Hoboken, NJ. John Wiley & Sons, Ltd.##David, H. A., and Nagaraja, H. N. (1998). Concomitants of order statistics. In Balakrishnan, N. and Rao, C. R., editors, Handbook of Statistics: Order Statistics: Theory & Methods, 16, 487-513. Elsevier, Amsterdam.##Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B(Methodological), 39(1), 1-38.##Henningsen, A., and Toomet, O. (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26(3), 443-458.##Izadi, M., and Khaledi, B.-E. (2007). Progressive {Type II censored order statistics and their concomitants: some stochastic comparisons results. J. Iran. Stat. Soc. (JIRSS), 6, 111-124.##Kundu, D., and Ganguly, A. (2017). Analysis of Step-Stress Models. Academic Press Inc., London, UK.##Laumen, B. (2017). Progressive Censoring and Stage Life Testing. PhD thesis, RWTH Aachen University.##Laumen, B., and Cramer, E. (2019a). Progressive censoring with fixed censoring times. Statistics, 53, 569-600.##Laumen, B., and Cramer, E. (2019b). Stage life testing. Nav. Res. Logistics, 53, 632-647.##Laumen, B., and Cramer, E. (2021a). k-step stage life testing. Statist. Neerlandica, 75, 203-223.##Laumen, B., and Cramer, E. (2021b). Stage life testing with random stage changing times. Commun. Statist. Theory Meth., DOI:10.1080/03610926.2020.1805764, to appear.## ##]
Prediction Based on Type-II Censored Coherent System Lifetime Data under a Proportional Reversed Hazard Rate Model
2
2
In this paper, we discuss the prediction problem based on censored coherent system lifetime data when the system structure is known and the component lifetime follows the proportional reversed hazard model. Different point and interval predictors based on classical and Bayesian approaches are derived. A numerical example is presented to illustrate the prediction methods used in this paper. Monte Carlo simulation study is performed to evaluate and compare the performances of different prediction methods.
153
181
Adeleh
Fallah
Adeleh
Fallah
Department of Statistics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
adeleh.fallah@gmail.com
Akbar
Asgharzadeh
Akbar
Asgharzadeh
Department of Statistics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
a.asgharzadeh@umz.ac.ir
Hon Keung Tony
Ng
Hon Keung Tony
Ng
Department of Statistical Science, Southern Methodist University, Dallas, Texas 75275-0332, USA
ngh@mail.smu.edu
Bayesian Predictor
Best Unbiased Predictor
Coherent System
Conditional Median Predictor
Maximum Likelihood Predictor
Prediction Intervals.
[Asgharzadeh, A. Fallah, A., Raqab, M. Z. and Valiollahi, R. (2018), Statistical inference based on Lindley record data. Statistical Papers, 59, 759-779.##Asgharzadeh, A., Valiollahi, R. and Kundu, D. (2015), Prediction for future failures in Weibull distribution under hybrid censoring. Journal of Statistical Computation and Simulation, 85, 824-838.##Balakrishnan, N., Ng, H. K. T. and Navarro, J. (2011a), Linear inference for Type-II censored lifetime data of reliability systems with known signatures. IEEE Transactions on Reliability, 60, 426--440.##Balakrishnan, N., Ng, H. K. T., and Navarro, J. (2011b), Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signatures. Journal of Nonparametric Statistics, 23, 741-752.##Bhattacharya and Samaniego (2010), Estimating component characteristics from system failure time data. Naval Research Logistics, 57, 380-389.##Basak, I., Basak, P., and Balakrishnan, N. (2006), On some predictors of times to failures of censored items in progressively censored sample. Computational Statistics and Data Analysis, 50, 1313-1337.##Basak, I., and N. Balakrishnan, N. (2017), Prediction of censored exponential lifetimes in a simple step-stress model under progressive Type II censoring. Computational Statistics, 32, 1665-1687.##Chahkandi, M., Ahmadi, J., and Baratpour, S. (2014), Non-parametric prediction intervals for the lifetime of coherent systems. Statistical Papers, 55, 1019-1034.##Chivers, C. (2012), MH adaptive: General Markov Chain Monte Carlo for Bayesian Inference using adaptive Metropolis-Hastings sampling, R package.##Kaminsky, K. S., and Rhodin, L. S. (1985), Maximum likelihood prediction. Annals of the Institute of Statistical Mathematics, 37, 507-517.##Kochar, S., Mukerjee, H., and Samaniego, F. J. (1999), The Signature of a Coherent System and its Application to Comparisons Among Systems. Naval Research Logistics, 46, 507-523.##https://doi.org/10.1002/(SICI)1520-6750(199908)46:5<507::AID-NAV4>3.0.CO;2-D##Navarro, J., and R. Rubio, R. (2010), Computations of coherent systems with five components. Communications in Statistics -- Simulation and Computation, 39, 68-84.##Navarro, J., Ruiz, J. M., and Sandoval, C. J. (2007), Properties of coherent systems with dependent components, Communications in Statistics - Theory and Methods, 36, 175-191.##Navarro, J., Samaniego, F. J., Balakrishnan, N., and Bhattacharya, D. (2008), On the application and extension of system signatures in engineering reliability. Naval Research Logistics, 55, 313-327.##Ng, H. K. T., Navarro, J., and Balakrishnan, N. (2012), Parametric inference from system lifetime data under a proportional hazard rate model. Metrika, 75, 367-388.##Raqab, M. Z., and Nagaraja, H. N. (1995), On some predictors of future order statistics. Metron, 53, 185-204.##Raqab, M. Z., Alkhalfan, L. A., Bdair, O. M., and Balakrishnan, N. (2019), Maximum likelihood prediction of records from 3-parameter Weibull distribution and some approximations. Journal of Computational and Applied Mathematics, 356, 118-132.##R Core Team (2019), R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.##Robert, C., and Casella, G. (2004), Monte Carlo Statistical Methods, 2nd edition. New York: Springer.##Saadati Nik, A., Asgharzadeh, A., and Raqab, M. Z. (2020), Prediction Methods for Future Failure Times Based on Type-II Right-Censored Samples from New Pareto-Type Distribution. Journal of Statistical Theory and Practice, 14, 39.##Samaniego, F. J. (1985), On closure of the IFR class under formation of coherent systems. IEEE Transactions on Reliability Theory, 34, 69-72.##Samaniego, F. J. (2007), System Signatures and their Applications in Engineering Reliability, International Series in Operations Research and Management Science 110. Springer, New York.##Yang, Y., Ng, H. K. T., and Balakrishnan, N. (2016), A stochastic expectation-maximization algorithm for the analysis of system lifetime data with known signature, Computational Statistics, 31, 609-641.##Yang, Y., Ng, H. K. T., and Balakrishnan, N. (2019), Expectation maximization algorithm for system based lifetime data with unknown system structure. AStA Advanced Statistical Analysis, 103, 69-98.##Zhang, J., Ng, H. K. T., and Balakrishnan, N. (2015a), Statistical inference of component lifetimes with location-scale distributions from censored system failure data with known signature. IEEE Transactions on Reliability, 64, 613-626.##Zhang, J., Ng, H. K. T., and Balakrishnan, N. (2015b), Tests for homogeneity of distributions of component lifetimes from system lifetime data with known system signatures. Naval Research Logistics, 62, 550-563.## ##]
Some New Results on Policy Limit Allocations
2
2
Suppose that a policyholder faces $n$ risks X1, ..., Xn which are insured under the policy limit with the total limit of l. Usually, the policyholder is asked to protect each Xi with an arbitrary limit of li such that ∑ni=1li=l. If the risks are independent and identically distributed with log-concave cumulative distribution function, using the notions of majorization and stochastic orderings, we prove that the equal limits provide the maximum of the expected utility of the wealth of policyholder. If the risks with log-concave distribution functions are independent and ordered in the sense of the reversed hazard rate order, we show that the equal limits is the most favourable allocation among the worst allocations. We also prove that if the joint probability density function is arrangement increasing, then the best arranged allocation maximizes the utility expectation of policyholder's wealth. We apply the main results to the case when the risks are distributed according to a log-normal distribution.
183
196
Sirous
Fathi Manesh
Sirous
Fathi Manesh
Department of Statistics, University of Kurdistan, Sanandaj, Iran
sirus_60@yahoo.com
Muhyiddin
Izadi
Muhyiddin
Izadi
Department of Statistics, Razi University, Kermanshah, Iran
izadi_552@yahoo.com
Baha-Eldin
Khaledi
Baha-Eldin
Khaledi
Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA
bkhaledi@fiu.edu
Arrangement Increasing Function
Log-Normal Distribution
Majorization
Schur-Convex Function
Stochastic Orders
Utility Function.
[Cheung, K. C. (2007), Optimal allocation of policy limits and deductibles. Insurance: Mathematics and Economics, 41, 382-391.##Denuit, M., and Vermandele, C. (1998), Optimal reinsurance and stop loss order. Insurance: Mathematics and Economics, 22, 229-233.##Denuit, M., Dhaene, J., Goovaerts, M. J., and Kaas, R. (2005), Actuarial Theory for Dependent Risks: Measures, Orders and Models. John Wiley & Sons, New york.##Hollander, M., Proschan, F., and Sethuraman, J. (1977), Functions decreasing in transposition and their applications in ranking problems. The Annals of Statistics, 5, 722-733.##Hua, L., and Cheung, K. C. (2008), Stochastic orders of scalar products with applications. Insurance: Mathematics and Economics, 42, 865-872.##Hu, S., and Wang, R. (2014), Stochastic comparisons and optimal allocation for policy limits and deductibles. Communications in Statistics-Theory and Methods, 43, 151-164.##Kaas, R., Goovaerts, M., Dhaene, J., and Denuit, M. (2008). Modern actuarial risk theory: using R. Springer Science & Business Media.##Klugman, S., Panjer, H., and Willmot, G. (2004), Loss Models: From Data to Decisions, second ed. John Wiley & Sons, New Jersey.##Lu, Z., and Meng, L. (2011), Stochastic comparisons for allocations of policy limits and deductibles with applications. Insurance: Mathematics and Economics, 48, 338-343.##Manesh F. S., and Khaledi, B. E. (2015), Allocations of policy limits and ordering relations for aggregate remaining claims. Insurance: Mathematics and Economics, 65, 9-14.##Marshall, A. W., Olkin, I., and Arnold, B. C. (2011), Inequalities: Theory of Majorization and its Applications. Springer, New York.##M"uller, A., and Stoyan, D. (2002), Comparison Methods for Stochastic Models and Risks. John Wiley & Sons, New York.##Pecaric, J. E., Proschan, F., and Tong, Y. L. (1992), Convex functions, partial orderings, and statistical applications. Academic Press, Inc. San Diego.##Shaked, M., and Shanthikumar, J. G. (2007), Stochastic Orders. Springer, New York.##Heerwaarden, A. E., Kaas, R., and Goovaerts, M. J. (1989), Optimal reinsurance in relation to ordering of risks. Insurance: Mathematics and Economics, 8, 11-17.## ##]
On the Blocks of Interpoint Distances
2
2
We study the blocks of interpoint distances, their distributions, correlations, independence and the homogeneity of their total variances. We discuss the exact and asymptotic distribution of the interpoint distances and their average under three models and provide connections between the correlation of interpoint distances with their vector correlation and test of sphericity. We discuss testing independence of the blocks based on the correlation of block interpoint distances. A homogeneity test of the total variances in each block and a simultaneous plot to visualize their relative ordering are presented.
197
218
Reza
Modarres
Reza
Modarres
Department of Statistics, George Washington University, Washington, DC, USA
reza@gwu.edu
Elliptical Model
Sphericity
Homogeneity
Total Variance.
[Anderson, T. W. (2003), An Introduction to Multivariate Statistical Analysis. New Jersey: Wiley-Interscience.##Bottesch, T., Bühler, T. Kächele, M. (2016), Speeding up k-means by approximating Euclidean distances via block vectors. Proceedings of the 33rd International Conference on International Conference on Machine Learning, Volume 48, 2578-2586.##Escoufier, Y. (1973), Le traitement des variables vectorielles. Biometrics, 29, 751-760.##Fang, K. T., Zhang, Y. T. (1990), Generalized multivariate analysis. Springer-Verlag, Berlin; Science Press, Beijing.##Flexer, A., Schnitzer, D. (2015), Choosing l_p norms in high-dimensional spaces based on hub analysis. Neurocomputing, 169, 281-287.##Freeman, J. and Modarres, R. (2005), Efficiency of test for independence after Box-Cox transformation. Journal of Multivariate Analysis, 95, 107-118.##Freeman, J. and Modarres, R. (2006), Inverse Box-Cox: The power-normal distribution. Statistics and Probability Letters, 76, 764-772.##Guo, L., Modarres, R. (2019), Interpoint Distance Classification of High Dimensional Discrete Observations. International Statistical Review, 87(2), 191-206.##Guo, L., Modarres, R. (2020), Nonparametric tests of independence based on interpoint distance. Journal of Nonparametric Statistics, 32 (1), 225-245.##Gupta, A. K. and Huang, W. J. (2002), Quadratic forms in skew normal variates. J. Math. Anal. Appl., 273, 558-564.##Iwashita, T. and Siotani, M. (1994), Asymptotic Distributions of Functions of a Sample Covariance Matrix under the Elliptical Distribution. The Canadian Journal of Statistics, 22 (2), 273-283.##Li, J. (2018), Asymptotic normality of interpoint distances for high-dimensional data with applications to the two-sample problem. Biometrika, 105 (3), 529-546.##Marozzi, M. (2015), Multivariate multidistance tests for high-dimensional low sample size case-control studies. Statistics in Medicine, 34, 1511-1526.##Marozzi, M. (2016), Multivariate tests based on interpoint distances with application to magnetic resonance imaging. Stat. Methods Med. Res., 25 (6), 2593-2610.##Marozzi, M., Mukherjee, A. and Kalina, J. (2020), Interpoint distance tests for high-dimensional comparison studies. J. Appl. Stat., 47 (4), 653-665.##Modarres, R. and Song, Y. (2020), Interpoint Distances: Applications, Properties and Visualization. Applied Stochastic Models in Business and Industry,##Modarres, R. (2020), Nonparametric Tests for Detection of High Dimensional Outliers. Submitted for publication.##Muirhead R. J. (1982), Aspects of Multivariate Statistical Theory, John Wiley & Sons, New York, NY.##Pal, A. K., Mondal, P. K., and Ghosh, A. K. (2016), High dimensional nearest neighbor classification based differences of inter-point distances. Pattern Recognition Letters, 74, 1-8.##Robert, P., Cl'eroux, R., and Ranger, N. (1985), Some results on vector correlation. Computational Statistics and Data Analysis, 3, 25-32.##Sarkar, S. and Ghosh, A. K. (2020), On Perfect Clustering of High Dimension, Low Sample Size Data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42(9), 2257-2272.##Song, Y. and Modarres, R. (2019), Interpoint Distance Test of Homogeneity for Multivariate Mixture Models. International Statistical Review, 87 (3), 613-638.##Srivastava, M. S. (2005), Some tests concerning the covariance matrix in high-dimensional data. Journal of Japan Statistical Society, 35, 251-272.##Srivastava, M. S. and Kubokawa, T. (2013), Tests for multivariate analysis of variance in high dimension under non-normality. Journal of Multivariate Analysis, 115, 204-216.## ##]
Stress-Strength and Ageing Intensity Analysis via a New Bivariate Negative Gompertz-Makeham Model
2
2
In Demography and modelling mortality (or failure) data the univariate Makeham-Gompertz is well-known for its extension of exponential distribution. Here, a bivariate class of Gompertz--Makeham distribution is constructed based on random number of extremal events. Some reliability properties such as ageing intensity, stress-strength based on competing risks are given. Also dependence properties such as dependence structure, association measures and tail dependence measures are obtained. A simulation study and a performance analysis is given based on estimators such as MLE, Tau-inversion and Rho-inversion.
219
246
Hossein-Ali
Mohtashami Borzadaran
Hossein-Ali
Mohtashami Borzadaran
Department of Statistics, Ordered Data, Reliability and Dependency Center of Excellence, Ferdowsi University of Mashhad, Mashhad, Iran
h.mohtashami@mail.um.ac.ir
Hadi
Jabbari
Hadi
Jabbari
Department of Statistics, Ordered Data, Reliability and Dependency Center of Excellence, Ferdowsi University of Mashhad, Mashhad, Iran
jabbarinh@um.ac.ir
Mohammad
Amini
Mohammad
Amini
Department of Statistics, Ordered Data, Reliability and Dependency Center of Excellence, Ferdowsi University of Mashhad, Mashhad, Iran
m-amini@um.ac.ir
Ali
Dolati
Ali
Dolati
Department of Statistics, Ordered Data, Reliability and Dependency Center of Excellence, Ferdowsi University of Mashhad, Mashhad, Iran
dolati50@yahoo.com
Bivariate Exponential Distribution
Demography
Survival Function
Hazard Function.
[Abd El-Bar, A. M. (2018), An extended gompertz-makeham distribution with application to lifetime data. Communications in Statistics-Simulation and Computation, 47(8), 2454-2475.##Adham, S. A., and Walker, S. G. (2001), A multivariate Gompertz-type distribution. Journal of Applied Statistics. 28(8), 1051-1065.##Anderson, J. E., Louis, T. A., Holm, N. V., and Harvald, B. (1992), Time-dependent association measures for bivariate survival distributions. Journal of the American Statistical Association, 87(419), 641-650.##Bailey, R. C., and Homer, L. D. (1977), Computations for a best match strategy for kidney transplantation. Transplantation, 23(4), 329-336.##Bailey, R. C., Homer, L. D., and Summe, J. P. (1977), A proposal for the analysis of kidney graft survival. Transplantation, 24(5), 309-315.##Bebbington, M., Green, R., Lai, C. D., and Zitikis, R. (2014), Beyond the Gompertz law: exploring the late-life mortality deceleration phenomenon. Scandinavian Actuarial Journal, 2014(3), 189-207.##Clayton, D. G. (1978), A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65(1), 141-151.##Denuit, M., Dhaene, J., Goovaerts, M., and Kaas, R. (2006), Actuarial theory for dependent risks: measures, orders and models. John Wiley & Sons.##El-Sherpieny, E. A., Ibrahim, S. A., and Bedar, R. E. (2013), A new bivariate distribution with generalized Gompertz marginals. Asian Journal of Applied Sciences, 1(04), 141-150.##Feng, X., and He, G. (2008), Estimation of parameters of the Makeham distribution using the least squares method. Mathematics and Computers in Simulation , 77(1), 34-44.##Golubev, A. (2009), How could the Gompertz--Makeham law evolve. Journal of theoretical Biology, 258(1), 1-17.##Gompertz, B. (1825), XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. FRS & c. Philosophical transactions of the Royal Society of London, 115, 513-583.##Jiang, R., Ji, P., and Xiao, X. (2003), Aging property of unimodal failure rate models. Reliability Engineering & System Safety, 79(1), 113-116.##Johnson, N. L., and Kotz, S. (1975), A vector multivariate hazard rate. Journal of Multivariate Analysis, 5(1), 53-66.##Johnson, N., Kotz, S., and Balakrishnan, N. (1994), Continuous Univariate Distributions. Volume 1, 2nd Edition. John Wiley and Sons, New York.##Johnson, N. L., Kotz, S., and Balakrishnan, N. (1997), Discrete multivariate distributions. Volume 165. Wiley. John Wiley and Sons (New York).##Juckett, D. A., and Rosenberg, B. (1993), Comparison of the Gompertz and Weibull functions as descriptors for human mortality distributions and their intersections. Mechanisms of Ageing and Development, 69(1-2), 1-31.##Kolev, N. (2016), Characterizations of the class of bivariate Gompertz distributions. Journal of Multivariate Analysis, 148, 173-179.##Lai, C. D., and Xie, M. (2006), Stochastic ageing and dependence for reliability . Springer Science & Business Media.##Marshall, A. W., and Olkin, I. (1997), A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84(3), 641-652.##Marshall, A. W., and Olkin, I. (2007), Life distributions. Springer, New York.##Marshall, A. W., and Olkin, I. (2015), A bivariate Gompertz--Makeham life distribution. Journal of Multivariate Analysis, 139, 219-226.##Melnikov, A., and Romaniuk, Y. (2006), Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts. Insurance: Mathematics and Economics, 39(3), 310-329.##Missov, T. I., and Lenart, A. (2013), Gompertz--Makeham life expectancies: expressions and applications. Theoretical Population Biology, 90, 29-35.##Nelsen, R. B. (2007), An introduction to copulas. Springer Science & Business Media.##Oakes, D. (1989), Bivariate survival models induced by frailties. Journal of the American Statistical Association, 84(406), 487-493.##Scollnik, D. P. M. (1995), Simulating random variates from Makeham's distribution and from others with exact or nearly log--concave densities. Transactions of the Society of Actuaries, 47, 409-437.##Shih, J. H., and Emura, T. (2019), Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula. Statistical Papers, 60(4), 1101-1118.##Szymkowiak, M. (2020), Lifetime Analysis by Aging Intensity Functions. Springer International Publishing.##Wang, J. L., Muller, H. G., and Capra, W. B. (1998), Analysis of oldest-old mortality: Life--tables revisited. The Annals of Statistics, 26(1), 126-163.## ##]
Finite Sample Properties of Quantile Interrupted Time Series Analysis: A Simulation Study
2
2
Interrupted Time Series (ITS) analysis represents a powerful quasi-experime-ntal design in which a discontinuity is enforced at a specific intervention point in a time series, and separate regression functions are fitted before and after the intervention point. Segmented linear/quantile regression can be used in ITS designs to isolate intervention effects by estimating the sudden/level change (change in intercept) and/or the gradual change (change in slope). To our knowledge, the finite-sample properties of quantile segmented regression for detecting level and gradual change remains unaddressed. In this study, we compared the performance of segmented quantile regression and segmented linear regression using a Monte Carlo simulation study where the error distributions were: IID Gaussian, heteroscedastic IID Gaussian, correlated AR(1), and T (with 1, 2 and 3 degrees of freedom, respectively). We also compared segmented quantile regresison and segmented linear regression when applied to a real dataset, employing an ITS design to estimate intervention effects on daily-mean patient prescription volumes. Both the simulation study and applied example illustrate the usefulness of quantile segmented regression as a complementary statistical methodolo-gy for assessing the impacts of interventions in ITS designs.
247
267
Rahim
Moineddin
Rahim
Moineddin
Department of Family and Community Medicine, Faculty of Medicine, University of Toronto, 500 University Avenue, Toronto, Ontario M5G 1V7, Canada
Rahim.moineddin@utoronto.ca
Christopher
Meaney
Christopher
Meaney
Department of Family and Community Medicine, Faculty of Medicine, University of Toronto, 500 University Avenue, Toronto, Ontario M5G 1V7, Canada
Christopher.Meaney@utoronto.ca
Sumeet
Kalia
Sumeet
Kalia
Department of Family and Community Medicine, Faculty of Medicine, University of Toronto, 500 University Avenue, Toronto, Ontario M5G 1V7, Canada
Sumeet.Kalia@utoronto.ca
Interrupted Time-Series
Segmented Linear Regression
Segmented Quanti-le Regression
Monte Carlo Simulation Study.
[Astivia, O. L. O., and Zumbo, B. D. (2019), Heteroskedasticity in Multiple Regression Analysis: What it is, How to Detect it and How to Solve it with Applications in R and SPSS. Practical Assessment, Research, and Evaluation, 24(1).##Austin, P. C., and Tu, J. V., and Daly, P. A., and Alter, D. A. (2005), The use of quantile regression in health care research: a case study examining gender differences in the timeliness of thrombolytic therapy. Statistics in medicine, 24(5), 791-816.##Baltagi, B. H. (2010), Econometrics. Springer.##Burton, A., and Altman, D. G., and Royston, P., and Holder, R. L. (2006), The design of simulation studies in medical statistics. Statistics in medicine, 25(24), 4279-4292.##Campbell, D. T., and Stanley, J. C. (2015), Experimental and quasi-experimental designs for research. Ravenio Books.##Cook, T. D., and Campbell, D. T., and Day, A. (1979), Quasi-experimentation: Design & analysis issues for field settings. Houghton Mifflin Boston.##Ferron, J., and Rendina-Gobioff, G. (2005), Interrupted time series design. Encyclopedia of Statistics in Behavioral Science.##Geraci, M., and Bottai, M. (2007), Quantile regression for longitudinal data using the asymmetric Laplace distribution. Biostatistics, 8(1), 140-154.##Gillings, D., and Makuc, D., and Siegel, E. (1981), Analysis of interrupted time series mortality trends: an example to evaluate regionalized perinatal care. American journal of public health, 71(1), 38-46.##Honda, T. (2013), Nonparametric quantile regression with heavy-tailed and strongly dependent errors. Annals of the Institute of Statistical Mathematics, 65(1), 23-47.##Kezdi, G. (2003), Robust standard error estimation in fixed-effects panel models. Available at SSRN 596988 .##Kocherginsky, M., and He, X., and Mu, Y. (2005), Practical confidence intervals for regression quantiles. Journal of Computational and Graphical Statistics, 14(1), 41-55.##Koenker, R. (2005), Quantile Regression. Cambridge.##Koenker, R., and Bassett Jr, G. (1978), Regression quantiles. Econometrica: journal of the Econometric Society, 33-50.##Koenker, R., and Chernozhukov, V., and He, X., and Peng, L. (2017), Handbook of quantile regression . CRC press.##Koenker, R., and Hallock, K. F. (2001), Quantile regression. Journal of economic perspectives, 15(4), 143-156.##Nolan, J., P and Ojeda-Revah, D. (2013), Linear and nonlinear regression with stable errors. Journal of Econometrics, 172(2), 186-194.##Sherman, M. (1997), Comparing the sample mean and the sample median: An exploration in the exponential power family. The American Statistician, 51(1), 52-54.##Tarr, G. (2012), Small sample performance of quantile regression confidence intervals. Journal of Statistical Computation and Simulation, 82(1), 81-94.##Wagner, A. K., and Soumerai, S. B., and Zhang, F., and Ross-Degnan, D. (2002), Segmented regression analysis of interrupted time series studies in medication use research. Journal of clinical pharmacy and therapeutics, 27(4), 299-309.##Xiong, W., and Tian, M. (2019), Weighted quantile regression theory and its application. Journal of Data Science, 17(1), 145-160.##Yang, X. R., and Zhang, L. X., (2008), A note on self-weighted quantile estimation for infinite variance quantile autoregression models. statistics & probability letters, 78(16), 2731-2738.## ##]
Applications of TP2 Functions in Theory of Stochastic Orders: A Review of some Useful Results
2
2
In the literature on Statistical Reliability Theory and Stochastic Orders, several results based on theory of TP2/RR2 functions have been extensively used in establishing various properties. In this paper, we provide a review of some useful results in this direction and highlight connections between them.
269
287
Sameen
Naqvi
Sameen
Naqvi
Department of Mathematics, Indian Institute of Technology Hyderabad, Kandi, India
sameen@math.iith.ac.in
Neeraj
Misra
Neeraj
Misra
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India
neeraj@iitk.ac.in
Ping Shing
Chan
Ping Shing
Chan
Department of Statistics, The Chinese University of Hong Kong, New Territories, Hong Kong
benchan@cuhk.edu.hk
Hazard Rate Order
Likelihood Ratio Order
Reversed Hazard Rate Order
RR2
TP2
[Aboukalam, F., and Kayid, M. (2007), Some new results about shifted hazard and shifted likelihood ratio orders. In International Mathematical Forum, 31, 1525-1536.##Artin, E. (1931), Einfuhrung in die Theorie der Gamma-funktion. BG Teubner.##Barlow, R. E., and Proschan, F. (1975), Statistical theory of Reliability and life testing: Probability Models. New York: Holt, Rinehart, and Winston.##Bartoszewicz, J. (1998), Applications of a general composition theorem to the star order of distributions. Statistics & probability letters, 38(1),1-9.##Belzunce, F., Ruiz, J. M., and Ruiz, M. C. (2002), On preservation of some shifted and proportional orders by systems. Statistics & probability letters, 60(2), 141-154.##Belzunce, F., Martinez-Riquelme, C., and Muler, J. (2016), An Introduction to Stochastic Orders. Academic Press, Elsevier.##Bergmann, R. (1991), Stochastic orders and their application to a unified approach to various concepts of dependence and association. Institute of Mathematical Statistics Lecture Notes-Monograph Series, 48-73.##Brown, M., and Shanthikumar, J. G. (1998), Comparing the variability of random variables and point processes. Probability in the Engineering and Informational Sciences, 12, 425-444.##Dasgupta, S., and Sarkar, S. K. (1984), On TP2 and log-concavity. In Inequalities in Statistics and Probability, Lecture Notes-Monograph Series/ Institute of Mathematical Statistics, 54-58.##Dewan, I., and Khaledi, B. E. (2014), On stochastic comparisons of residual life time at random time. Statistics & Probability Letters, 88, 73-79.##Di Crescenzo, A., and Longobardi, M. (2001), The up reversed hazard rate stochastic order. Scientiae Mathematicae Japonicae, 54(3), 575-581.##Durham, S., Lynch, J. and Padgett, W. J. (1990), TP2-orderings and the IFR property with applications. Probability in the Engineering and Informational Sciences, 4(1), 73-88.##Hu, T., and Zhu, Z. (2001), An analytic proof of the preservation of the up-shifted likelihood ratio order under convolutions. Stochastic Process. Appl., 95, 55-61.##Joag-dev, K., Kochar, S., and Proschan, F. (1995), A general composition theorem and its applications to certain partial orderings of distributions. Statistics & Probabality Letters, 22,111-119.##Karlin, S. (1968), Total positivity (Vol. 1). Stanford: Stanford University Press.##Keilson, J., and Sumita, U. (1982), Uniform stochastic ordering and related inequalities. Canadian Journal of Statistics, 10(3), 181-198.##Khaledi, B. E., and Shaked, M. (2010), Stochastic comparisons of multivariate mixtures. J Multivariate Anal, 101, 2486-2498.##Khaledi, B. E. (2014), Karlin's basic composition theorems and stochastic orderings. Journal of the Iranian Statistical Society, 13(2),177-186.##Lai, C., and Xie, M. (2006), Stochastic ageing and dependence for reliability. Springer.##Laradji, A. (2015), Sums of totally positive functions of order 2 and applications. Statistics & Probability Letters, 105, 176-180.##Lehmann, E. L. (1966), Some concepts of dependence. The Annals of Mathematical Statistics, 1137-1153.##Li, H., and Li, X. (2013), Stochastic orders in reliability and risk. In Honor of Professor Moshe Shaked. Springer.##Lillo, R. E., Nanda, A. K., and Shaked, M. (2000), Some shifted stochastic orders. In Recent advances in reliability theory (85-103). Birkhauser, Boston, MA.##Lillo, R. E., Nanda, A. K., and Shaked, M. (2001), Preservation of some likelihood ratio stochastic orders by order statistics. Statistics & Probability Letters, 51(2), 111-119.##Lynch, J., Mimmack, G., and Proschan, F. (1987), Uniform stochastic orderings and total positivity. Canadian Journal of Statistics, 15(1), pp.63-69.##Lynch, J. D. (1999), On conditions for mixtures of increasing failure rate distributions to have an increasing failure rate. Probability in the Engineering and Informational Sciences, 13(1), 33-36.##Marshall, A. W., Olkin, I., and Arnold, B. C. (2010), Total Positivity, In: Inequalities: theory of majorization and its applications, 757-768, Springer.##Misra, N., and Naqvi, S. (2018), Some unified results on stochastic properties of residual lifetimes at random times. Brazilian Journal of Probability and Statistics, 32(2), 422-436.##Mosler, K., and Scarsini, M. (2012), Stochastic orders and applications: a classified bibliography (401). Springer Science & Business Media.##Muller, A., and Stoyan, D. (2002), Comparison methods for stochastic models and risks (389). Wiley.##Nakai, T. (1995), A partially observable decision problem under a shifted likelihood ratio ordering, Mathematical and Computer Modelling, 22, 237-246.##Nanda, A. K., Bhattacharjee, S., and Alam, S. S. (2006), On upshifted reversed mean residual life order. Communications in Statistics-Theory and Methods, 35(8), 1513-1523.##Pr'ekopa, A. (1971), Logarithmic concave measures with application to stochastic programming. Acta Scientiarum Mathematicarum, 32, 301-316.##Pecaric, J. E., Proschan, F., and Tong, Y. L. (1992), Convex functions, partial orderings, and statistical applications, ser. Math. Sci. Engrg. Boston, MA: Academic Press, Inc, New York.##Shaked, M., and Shanthikumar, J. G. (2007), Stochastic Orders. New York: Springer.##Shanthikumar, J. G., and Yao, D. D. (1986), The preservation of likelihood ratio ordering under convolutions. Stochastic Processes and Their Applications, 23, 259-267.##Szekli, R. (2012), Stochastic ordering and dependence in applied probability (97). Springer Science & Business Media.##Tong, Y. L. (2012), The multivariate normal distribution. Springer Science & Business Media.##Whitt, W. (1988), Stochastic orderings. Encyclopedia of the Statistical Sciences Vol. 8, S. Kotz and N.L. Johnson, editors, 832-836, Wiley, New York.## ##]
Matrix-Variate Beta Generator - Developments and Application
2
2
Matrix-variate beta distributions are applied in different fields of hypothesis testing, multivariate correlation analysis, zero regression, canonical correlation analysis and etc. A methodology is proposed to generate matrix-variate beta generator distributions by combining the matrix-variate beta kernel with an unknown function of the trace operator. Several statistical characteristics, extensions and developments are presented. Special members are then used in a univariate and multivariate Bayesian analysis setting. These models are fitted to simulated and real datasets, and their fitting and performance are compared to well-established competitors.
289
306
Janet van
Niekerk
Janet van
Niekerk
University of Pretoria, Department of Statistics, Pretoria, South Africa
janet.vanniekerk@up.ac.za
Andriette
Bekker
Andriette
Bekker
University of Pretoria, Department of Statistics, Pretoria, South Africa
Andriette.Bekker@up.ac.za
Mohammad
Arashi
Mohammad
Arashi
Ferdowsi University of Mashhad, Department of Statistics, Mashhad, Iran
arashi@um.ac.ir
Bayesian Analysis
Binomial
Eigenvalues
Gaussian Sample
Gibbs Sampling
Matrix-Variate Beta
[Bekker, A., Roux, J. J. J., Ehlers, R., and Arashi, M. (2012), Distribution of the product of determinants of noncentral bimatrix beta variates. Journal of Multivariate Analysis, 109, 73-87.##Bekker, A., Van Niekerk, J., and Arashi, M. (2017), Wishart distributions: Advances in theory with Bayesian application. Journal of Multivariate Analysis, 155, 272-283.##Chikuse, Y. (1980), Invariant polynomials with matrix arguments and their applications. Multivariate Statistical Analysis, 1, 54-68.##Davis, A. W. (1979), Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory. Annals of the Institute of Statistical Mathematics, 31(A), 465-485.##Ehlers, R. (2011), Bimatrix Variate Distributions of Wishart Ratios With Application. Unpublished PhD Dissertation, University of Pretoria, South Africa.##Gupta, A.K. and Nagar, D.K. (2000), Matrix-variate beta distribution. International Journal of Mathematical Sciences, 24(7), 449-459.##Gupta, A. K., and Nagar, D. K. (2006), A generalized matrix-variate beta distribution. International Journal of Applied Mathematical Sciences, 31(1), 21-36.##Gupta, A. K., and Nagar, D. K. (2009), Properties of matrix-variate beta type 3 distribution. International Journal of Mathematical Sciences, http://dx.doi.org/10.1155/2009/308518.##Muirhead, R. J. (2005), Aspects of Multivariate Statistical Theory. New York: Wiley.##Nadarajah, S., and Kotz, S. (2006), Some beta distributions. Bulletin of the Brazilian Mathematical Society, 31(1), 103-125.##Nagar, D. K., and Gupta, A. K. (2002), Matrix-variate Kummer-beta distribution. Journal of the Australian Mathematical Society, 73(1), 11-26.##Nagar, D. K., Rold'a-Correa, A., and Gupta, A. K. (2013), Extended matrix-variate gamma and beta functions. Journal of Multivariate Analysis, 122, 53-69.##Nagar, D. K., Arashi, M., and Nadarajah, S. (2017), Bimatrix variate gamma-beta distributions. Communications in Statistics - Theory and Methods, 46(9), 4464-4483.##Ng, K. W., and Kotz, S. (1995), Kummer-gamma and Kummer-beta univariate and multivariate distributions. Research report, The University of Hong Kong, Hong Kong.##Pham-Gia, T., Phong, D. T., and Thanh, D. N. (2020), Distributions of powers of the central beta matrix variates and applications. Statistical Methods and Applications, 29(3), 651-668.##Tounsi, M. (2019), The Extended Matrix-Variate Beta Probability Distribution on Symmetric Matrices. Methodology and Computing in Applied Probability,1-30.##Zine, R. (2012), On the matrix-variate beta distribution. Communications in Statistics- Theory and Methodology, 41(9), 1569-1582.## ##]
Sampling of Multiple Variables Based on Partially Ordered Set Theory
2
2
We introduce a new method for ranked set sampling with multiple criteria. The method relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, units are ranked in sets based on linear extensions in partially order set theory with considering all variables simultaneously. Results willbe evaluated by a relatively extensive simulation studies on Bivariate normal distribution and two real case studies on commercial and medicinal use of flowers, and the pollution of herb-layer by Lead, Cadmium, Zinc and Sulfur in some regions of the southwest of Germany.
307
331
Bardia
Panahbehagh
Bardia
Panahbehagh
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
panahbehagh@khu.ac.ir
Rainer
Bruggemann
Rainer
Bruggemann
Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Berlin, Germany
brg_home@web.de
Mohammad
Salehi
Mohammad
Salehi
Department of Mathematics, Statistics and Physics, Qatar University, P. O. Box 2713, Doha, Qatar
salehi@qu.edu.qa
Environmental Pollution
Linear Extension
Medicinal Use of Flowers
Multiple Variables Ranked Set Sampling
Partially Order Set
Theory.
[Al-Saleh, M., and Zheng, G. (2002), Estimation of bivariate characterstics using ranked set sampling. Australian & New Zealand Jurnal of Statistics, 44, 221-232.##Bruggemann, R., and Carlsen, L. (2011), An Improved Estimation of Averaged Ranks of Partial Orders. MATCH Comm. Math. Comput. Chem. 65, 383-414.##Brüggemann, R., Kaune, A., and Voigt. K. (1996), Vergleichende ökologische Bewertung von Regionen in Baden- Württemberg. Pages 455-467 in Landesanstalt für Umweltschutz Baden-Württemberg, ed. 4.Statuskolloquium, Projekt "Angewandte Ökologie" Nr. 16. Präzis-Druck Karlsruhe, Karlsruhe.##Bruggemann, R., Mucha, H. J., and Bartel, H. G. (2013), Ranking of Polluted Regions in South West Germany Based on a Multi-indicator System. MATCH Commun. Math. Comput. Chem., 69,433-462.##Bruggemann, R., and Patil, G. P. (2011), Ranking and Prioritization with Multi- Indicator Systems, Introduction to Partial Order and Its Applications, Springer, New York.##Bruggemann, R., Pudenz S., Voigt K., Kaune A., and Kreimes K. (1999), An algebraic/graphical tool to compare ecosystems with respect to their pollution. IV: Comparative regional analysis by Boolean arithmetic. Chemosphere, 38, 2263-2279.##Bruggemann, R., Sorensen, P. B., Lerche, D., and Carlsen, L. (2004), Estimation of Averaged Ranks by a Local Partial Order Model. J. Chem. Inf. Comp. Sc. 44, 618-625.##Bruggemann, R., Voigt, K., Kaune, A., Pudenz, S., Komossa, D., and Friedrich, J. (1998), Vergleichende ökologische Bewertung von Regionen in Baden- Württemberg GSF-Bericht 20/98. GSF, Neuherberg.##Bruggemann, R., Welzl, G., and Voigt, K. (2003), Order Theoretical Tools for the Evaluation of Complex Regional Pollution Patterns. J. Chem. Inf. Comp. Sc., 43, 1771-1779.##Bubley, R., and Dyer, M. (1999), Faster random generation of linear extensions. Discr. Math., 201, 81-88.##Chen, Z., Bai, Z., and Sinha, B. (2004), Ranked set sampling: theory and applications. Lecture Notes in Statistics, Springer, New York.##Chen, Z., and Shen, L. (2003), Two-layer ranked set sampling with concomitant variables. Journal of Statistical Planning and Inference, 115, 45-57.##David, H. A., and Nagaraja, H. N. (2003), Order Statistic, third ed. Wiley, New York.##De Loof, K., De Baets, B., and De Meyer, H. (2011), Approximation of Average Ranks in Posets. MATCH Commun. Math. Comput. Chem., 66, 219-229.##Environmental Protection Agency Baden-Wurttemberg, (1994), Signale aus der Natur 10 Jahre Okologisches Wirkungskataster Baden-Wurttemberg. Kraft Druck GmbH, Ettlingen.##McIntyre, G. A. (1952), A method of unbiased selective sampling. using ranked sets. Australian Journal of Agricultural Research, 3, 385-390.##Norris, R. C., Patil, G. P., and Sinha, A. K. (1995), Estimation of multiple characteristics by ranked set sampling methods. Coenoses, 10, 95-111.##Panahbehagh, B., Bruggemann R., Parvardeh, A., Salehi, M., and Sabzalian, M. R. (2018), An unbalanced ranked set sampling to get more than one sample from each set. Journal of Survey Statistics and Methodology, 6(3), 285-305.##Patil, G. P., Sinha, A. K., and Taillie, C. (1994), Ranked set sampling for multiple characteristics. International Journal of Ecology and Environmental Sciences, 20, 94-109.##Patil, G. P., Sinha, A. K., and Taillie, C. (1999), Ranked set sampling: A bibliography. Environmental and Ecological Statistics, 6, 91-98.##Patil, G. P., Sinha, A. K., and Taillie, C. (1994), Ranked set sampling, in Handbook of Statistics, Environmental Statistics, Vol. 12, G.P. Patil and C.R. Rao, eds, NorthHolland, Amsterdam.##Ridout, M. S. (2003), On ranked set sampling for multiple characterestics. Environmental and Ecological Statistics, 10, 225-262.##Samawi, H. M. (1996), Stratified ranked set sample. Pakistan Journal of Statistics, 12, 9-16.##Sarndal, C. E., Swensson, B., and Wretman, J. (1992), Model Assisted Survey Sampling, New York, Springer.##Yang, S. S. (1977), General distribution theory of the concomitants of order statistics. The Annals of Statistics, 5, 996-1002.## ##]
An Alternative to the Beta-Binomial Distribution with Application in Developmental Toxicology
2
2
The beta-binomial distribution is resulted when the probability of success per trial in the binomial distribution varies in successive trials and the mixing distribution is from the beta family. For experiments with binary outcomes, often it may happen that observations exhibit some extra binomial variation and occur in clusters. In such experiments the beta-binomial distribution can generally provide an adequate fit to the data. Here, we introduce an alternative when the mixing distribution is assumed to be from the log-Lindley family. The properties of this new model are explored and it is shown that similar to the beta-binomial distribution, the log-Lindley binomial distribution can also be applied in modeling clustered binary outcomes. An example with real experimental data from a developmental toxicity experiment is utilized to provide further illustration.
333
345
Mehdi
Razzaghi
Mehdi
Razzaghi
Department of Mathematics, Bloomsburg University, Bloomsburg, PA, USA
mrazzagh@bloomu.edu
Beta-Binomial
Clustered Binary Outcomes
Distribution Mixtures. Extra Binomial Variation
Log-Lindley.
[Berson, E. L., Rosner, B., and Simonoff, E. (1980), An outpatient population of retinitis pigmentosa and their normal relatives: risk factors for genetic typing and detection derived from their ocular examination. American Journal of Ophthalmology, 89, 763-775.##Chen, J. J., and Kodell, R. L. (1989), Quantitative risk assessment for teratological effects. Journal of the American Statistical Association, 84, 966-971.##Gomez-Deniz, E., Sordo, M. A., and Calderin-Ojeda, E. (2014), The log-Lindley distribution as an alternative to the beta regression model with applications in insurance. Insurance: Mathematics and Economics, 54, 49-57.##Grassia, A. (1977). On a family of distributions with argument between 0 and 1 obtained by transformation of the gamma and derived compound distributions. Australian Journal of Statistics, 19, 108-114.##Jorda, P., and Jimenez-Gamero, M. D. (2016). A note on the log-Lindley distribution. Insurance: Mathematics and Economics, 71, 189-194.##Lindley, D. V. (1958). Fiducial distribution and Bayes' theorem. Journal of the Royal Statristical Society, Series B, 20, 102-107.##Lindley, D. V. (1965). Introduction to Probability and Statistics from a Bayesian Viewpoint, Part II: Inference. Cambridge University Press, New York.##Nocedal, J., and Wright, S. J (1999). Numerical Optimization. Springer, New York.##R Core Team (2012). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org/##Razzaghi, M. (2020). Statistical Models in Toxicology. CRC Press, Boca Raton, FL.##Rosner, B. (1982). Statistical methods in ophthalmology: an adjustment for the intra-class correlation between eyes. Biometrics, 38, 105-114.##Smith, D. M. (1983). Maximum likelihood estimation of the parameters of the beta-binomial distribution. Applied Statistics, 32, 192-204.##Statistical Analysis System SAS (2014). Version 9.4. Cary, NC: SAS Institute Inc.##Wilcox, R. E. (1981), A review of the beta-binomial model and its extensions. Journal of Educational Statistics, 6, 3-32.##Williams, D. A. (1975), The analysis of binary responses from teratological experiments involving reproduction and teratogenicity. Biometrics, 31, 949-952.##Zakerzadeh, H., and Dolati, A. (2009), Generalized Lindley distribution. Journal of mathematical Extension, 3, 13-25.## ##]
Conditional Dependence in Longitudinal Data Analysis
2
2
Mixed models are widely used to analyze longitudinal data. In their conventional formulation as linear mixed models (LMMs) and generalized LMMs (GLMMs), a commonly indispensable assumption in settings involving longitudinal non-Gaussian data is that the longitudinal observations from subjects are conditionally independent, given subject-specific random effects. Although conventional Gaussian LMMs are able to incorporate conditional dependence of longitudinal observations, they require that the data are, or some transformation of them is, Gaussian, a serious limitation in a wide variety of practical applications. Here, we introduce the class of Gaussian copula conditional regression models (GCCRMs) as flexible alternatives to conventional LMMs and GLMMs. One advantage of GCCRMs is that they extend conventional LMMs and GLMMs in a way that reduces to conventional LMMs, when the data are Gaussian, and to conventional GLMMs, when conditional independence is assumed. We implement likelihood analysis of GCCRMs using existing software and statistical packages and evaluate the finite-sample performance of maximum likelihood estimates for GCCRM empirically via simulations vis-a-vis the `naive' likelihood analys is that incorrectly assumes conditionally independent longitudinal data. Our results show that the `naive' analysis yields estimates with possibly severe bias and incorrect standard errors, leading to misleading inferences. We use bolus count data on patients' controlled analgesia comparing dosing regimes and data on serum creatinine from a renal graft study to illustrate the applications of GCCRMs.
347
370
Mahmoud
Torabi
Mahmoud
Torabi
Departments of Community Health Sciences and Statistics, University of Manitoba, Winnipeg, Manitoba, CANADA R3E 0W3
Mahmoud.Torabi@umanitoba.ca
Alexander
R. de Leon
Alexander
R. de Leon
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, CANADA T2N 1N4
adeleon@ucalgary.ca
Exponential Family
Gaussian Copula
Marginal Distribution
Maximum Likelihood Estimation
Random Effects
[Brown, H. and Prescott, R. (2015). Applied Mixed Models in Medicine. New York: John Wiley & Sons.##Clemen, R. and Reilly, T. (1999). Correlation and copulas for decision and risk analysis. Management Science 45, 208-224.##Das, K., Li, R., Sengupta, S., and Wu, R. (2013). A Bayesian semiparametric model for bivariate sparse longitudinal data. Statistics in Medicine 32, 3899-3910.##de Leon, A. and Wu, B. (2011). Copula-based regression models for a bivariate mixed discrete and continuous outcome. Statistics in Medicine 30, 175-185.##Fieuws, S. and Verbeke, G. (2008). Predicting renal graft failure using multivariate longitudinal profiles. Biostatistics 9, 419-431.##Klaassen, C. and Wellner, J. (1997). E cient estimation in the bivariate normal copula: normal margins are least favourable. Bernoulli 3, 55-77.##Kugiumtzis, D. and Bora-Senta, E. (2010). Normal correlation coefficient of non-normal variables using piece-wise linear approximation. Computational Statistics 25, 645-662.##Magezi, D. A. (2015). Linear mixed-effects models for within-participant psychology experiments: an introductory tutorial and free, graphical user interface (LMMgui). Frontiers in Psychology 6(2), 1664-1078##Masarotto, G. and Varin, C. (2012). Gaussian copula marginal regression. Electronic Journal of Statistics 6, 1517-1549.##McCulloch, C. E., Searle, S. R., and Neuhaus, J. M. (2008). Generalized, Linear, and Mixed Models. New York: John Wiley & Sons.##Molenberghs, G. and Verbeke, G. (2005). Models for Discrete Longitudinal Data. New York: Springer.##R Core Team. (2020). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.##Renard, D., Geys, H., Molenberghs, G., Burzykowski, T., and Buyse, M. (2002). Validation of surrogate end points in multiple randomized clinical trials with discrete outcomes. Biometrical Journal 44, 921-935.##Searle, S. R., Casella, G., and McCulloch, C. E. (2006). Variance Components. New Jersey: John Wiley & Sons.##Vangeneugden, T., Molenberghs, G., Verbeke, G., and Demetrio, C. (2011). Marginal correlation from an extended random-effects model for repeated and overdispersed counts. Journal of Applied Statistics 38, 215-232.##Weiss, E. W. (2005). Modeling Longitudinal Data. New York: Springer.##Wu, B. and de Leon, A. R. (2014). Gaussian copula mixed models for clustered mixed outcomes, with application in developmental toxicology. Journal of Agricultural, Biological and Environmental Statistics 19, 39-56.##Wu, B., de Leon, A., and Withanage, N. (2013). Joint analysis of mixed discrete and continuous outcomes via copulas. In Analysis of Mixed Data: Methods and Applications, de Leon A and Carrie're Chough K (eds), 139-156, Chap 10. CRC/Chapman & Hall.##Young, J. H. (2002). Blood pressure and decline in kidney function: findings from the systolic hypertension in the elderly program (SHEP). Journal of the American Society of Nephrology 11, 2776-2782.## ##]