Volume 20, Issue 1 (6-2021)                   JIRSS 2021, 20(1): 1-26 | Back to browse issues page


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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
Abstract:   (699 Views)

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.

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Type of Study: Special Issue, Original Paper | Subject: 62Jxx: Linear inference, regression
Received: 2020/12/8 | Accepted: 2021/01/29 | Published: 2021/06/20

References
1. 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.
2. Ahmed, S. E. (2014), Penalty, Shrinkage and Pretest Strategies: Variable Selection and Estimation. Springer, New York, https://www.springer.com/gp/book/9783319031484.
3. Batista, G., and Monard, M. (2002), An analysis of four missing data treatment methods for supervised learning, Applied Artificial Intelligence, 17, 519-533.
4. Hoerl, A. E., and Kennard, R. W. (1970), Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67. [DOI:10.1080/00401706.1970.10488634]
5. Kaplan, E. L., and Meier, P. (1958), Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457-481. [DOI:10.1080/01621459.1958.10501452]
6. Koul, H., Susarla, V., and Van Ryzin, J. (1981), Regression analysis with randomly right censored data. The Annals of Statistics, 9, 1276-88. [DOI:10.1214/aos/1176345644]
7. Liang, H. (2006), Estimation in partially linear models and numerical comparisons. Computational Statistics and Data Analysis, 50(3), 675-685. [DOI:10.1016/j.csda.2004.10.007]
8. Liang, H., and Zhou, Y. (2008), Semiparametric Inference for ROC curves with censoring. Scandinavian Journal of Statistics, 35(2), 212-227. [DOI:10.1111/j.1467-9469.2007.00580.x]
9. Miller, R. G. (1976), Least squares regression with censored data. Biometrika, 63, 449-64. [DOI:10.1093/biomet/63.3.449]
10. Orbe, J., Ferreira, E., and Nunez-Anton, V. (2003), Censored Partial Regression. Biostatistics, 4(1), 109-121. [DOI:10.1093/biostatistics/4.1.109]
11. Ruppert, D., Wand, M. P., and Carroll, R. J. (2003), Semiparametric regression. Cambridge University Press, New York.
12. Schimek, M. G. (2000), Smoothing and Regression: Approaches, Computation and Application. John Wiley & Sons, Hoboken, NJ.
13. Shim, J. Y. (2005), Censored kernel ridge regression. Journal of the Korean Data and Information Science Society, 16(4), 1045-1052.
14. Stute, W. (1993), Consistent Estimation Under Random Censorship When Covariables Are Present. Journal Of Multivariate Analysis, 4, 89-103. [DOI:10.1006/jmva.1993.1028]
15. 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. [DOI:10.1142/S0218194007003173]
16. 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.

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