On the comparison of the pre-test and shrinkage phi-divergence test estimators for the symmetry model of categorical data

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Pardo, Leandro¹  Martin, Nirian² 

[1] Univ Complutense Madrid, Dept Stat & OR, E-28040 Madrid, Spain

[2] Univ Carlos III Madrid, Dept Stat, E-28903 Getafe, Madrid, Spain

关键词: Minimum phi-divergence estimator;    Phi-divergence statistics;    Preliminary test estimator;    Symmetry model;   

DOI  :  10.1016/j.cam.2010.07.026

来源: Elsevier

【 摘 要 】

The estimation problem of the parameters in a symmetry model for categorical data has been considered for many authors in the statistical literature (for example, Bowker (1948) [1], Ireland et al. (1969) [2], Quade and Salama (1975) [3] Cressie and Read (1988) [4], Menendez et al. (2005) [5]) without using uncertain prior information. It is well known that many new and interesting estimators, using uncertain prior information, have been studied by a host of researchers in different statistical models, and many papers have been published on this topic (see Saleh (2006) [9] and references therein). In this paper, we consider the symmetry model of categorical data and we study, for the first time, some new estimators when non-sample information about the symmetry of the probabilities is considered. The decision to use a restricted estimator or an unrestricted estimator is based on the outcome of a preliminary test, and then a shrinkage technique is used. It is interesting to note that we present a unified study in the sense that we consider not only the maximum likelihood estimator and likelihood ratio test or chi-square test statistic but we consider minimum phi-divergence estimators and phi-divergence test statistics. Families of minimum phi-divergence estimators and phi-divergence test statistics are wide classes of estimators and test statistics that contain as a particular case the maximum likelihood estimator, likelihood ratio test and chi-square test statistic. In an asymptotic set-up, the biases and the risk under the squared loss function for the proposed estimators are derived and compared. A numerical example clarifies the content of the paper. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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