1
1726-4057
Iranian Statistical Society
1
60: Probability theory and stochastic processes
Welcoming Message to the JIRSS
Zellner
Arnold
1
11
2002
1
1
1
5
10
07
2011
12
09
2015
It is a great honor to be invited to contribute to the first issue of the Journal of the Iranian Statistical Society. May the Journal and those associated with it have great success in attaining its goals and in furthering the progress of statistical science. While there has been worldwide recognition of the important role that statistics and statisticians play in producing progress in science and decision-making, some including Berger (2000) and Cox (2002) have expressed concerns that the field of statistics may be taken over by workers in other sciences who have established many statistical disciplines, e.g., biometrics, cliometrics, econometrics, psychometrics, sociometrics, etc. Indeed Sir David Cox in his invited Deming Lecture, presented at the August 2002 Joint Statistical Meetings in New York, pointed to extremely important contributions to statistics made by the geneticist R.A. Fisher, the physicist H. Jeffreys and the versatile scientist P.S. Laplace. While competition among various fields of science is hardly new, it is of course important to understand such competition and to be a winner and not a loser. ... To be continued in the attached file
84
60: Probability theory and stochastic processes
Modeling Nonnegative Data with Clumping at Zero: A Survey
Min
Yongyi
Agresti
Alan
1
11
2002
1
1
7
33
25
08
2011
12
09
2015
Applications in which data take nonnegative values but have a substantial proportion of values at zero occur in many disciplines. The modeling of such “clumped-at-zero” or “zero-inflated” data is challenging. We survey models that have been proposed. We consider cases in which the response for the non-zero observations is continuous and in which it is discrete. For the continuous and then the discrete case, we review models for analyzing cross-sectional data. We then summarize extensions for repeated measurement analyses (e.g., in longitudinal studies), for which the literature is still sparse. We also mention applications in which more than one clump can occur and we suggest problems for future research.
85
60: Probability theory and stochastic processes
Another View of the Classical Problem of Comparing Two Probabilities
Chernoff
Herman
1
11
2002
1
1
35
53
25
08
2011
12
09
2015
The usual calculation of the P-value for the classical problem of comparing probabilities is not always accurate. This issue arose in the context of a legal dispute which depended on when some written material was written in a diary. The problem raises some issues on the foundations of statistical inference.
86
60: Probability theory and stochastic processes
Location Reparameterization and Default Priors for Statistical Analysis
Fraser
D. A. S.
Yun Yi
Grace
1
11
2002
1
1
55
78
25
08
2011
12
09
2015
This paper develops default priors for Bayesian analysis that reproduce familiar frequentist and Bayesian analyses for models that are exponential or location. For the vector parameter case there is an information adjustment that avoids the Bayesian marginalization paradoxes and properly targets the prior on the parameter of interest thus adjusting for any complicating nonlinearity the details of this vector Bayesian issue will be investigated in detail elsewhere. As in wide generality a statistical model has an inference component structure that is approximately exponential or approximately location to third order, this provides general default prior procedures that can be described as reweighting likelihood in accord with a Jeffreys’ prior based on observed information. Two asymptotic models, that have variable and parameter of the same dimension and agree at a data point to first derivative conditional on an approximate ancillary, produce the same p-values to third order for inferences concerning scalar interest parameters. With some given model of interest there is then the opportunity to choose some second model to best assist the calculations or best achieve certain inference objectives. Exponential models are useful for obtaining accurate approximations while location models present possible parameter values in a direct measurement or location manner. We derive the general construction of the location reparameterization that gives the natural parameter of the location model coinciding with the given model to first derivative at a data point the derivation is in algorithmic form that is suitable for computer algebra. We then define a general default prior based on this location reparameterization this gives third order agreement between frequentist p-values and Bayesian survivor values in the vector case however, an adjustment factor is needed for component parameters that are not linear in the location parameterization. The general default prior can be difficult to calculate. But if we choose to work only to the secondorder, a Jeffreys’ prior based on the observed information function gives second order agreement between the frequentist p-values and Bayesian survivor values again adjustments are needed for parameters nonlinear in the vector location parameter the adjustment is a ratio of two nuisance information determinants, one for the nuisance parameter as given and one for the locally equivalent linear nuisance parameter.
87
60: Probability theory and stochastic processes
Parametric and Nonparametric Regression with Missing X’s—A Review
Toutenburg
Helge
Heumann
Christian
Nittner
Thomas
Scheid
Sandro
1
11
2002
1
1
77
109
25
08
2011
12
09
2015
This paper gives a detailed overview of the problem of missing data in parametric and nonparametric regression. Theoretical basics, properties as well as simulation results may help the reader to get familiar with the common problem of incomplete data sets. Of course, not all occurences can be discussed so this paper could be seen as an introduction to missing data within regression analysis and as an extension to the early paper of [19.
88
60: Probability theory and stochastic processes
On the Multivariate Rasch Model: Assessing Collaboration in Multiple Choice Tests
Vardi
Yahuda
Zhang
Chun-Hui
1
11
2002
1
1
111
126
25
08
2011
12
09
2015
We examine the Rasch model for latent structure para- meters in binary and
multiple response questionnaires and develop methodologies and data-analytic
tools for assessing collaboration/che- ating in multiple choice tests
89
60: Probability theory and stochastic processes
On Efficiency Criteria in Density Estimation
Bosq
Denis
1
11
2002
1
1
127
142
25
08
2011
12
09
2015
We discuss the classical efficiency criteria in density estimation and propose some variants. The context is a general density estimation scheme that contains the cases of i.i.d. or dependent random variables, in discrete or continuous time. Unbiased estimation, optimality and asymptotic optimality are considered. An example of a density estimator that satisfies some suggested criteria is given.
90
60: Probability theory and stochastic processes
Bayesian Nonparametric and Parametric Inference
Walker
Stephen G.
1
11
2002
1
1
143
163
25
08
2011
12
09
2015
This paper reviews Bayesian Nonparametric methods and discusses how parametric predictive densities can be constructed using nonparametric ideas.