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

Pardo Llorente, Leandro and Martín Apaolaza, Níriam (2011) 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, 235 (5). pp. 1160-1179. ISSN 0377-0427

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Minimum phi-divergence estimator; Phi-divergence statistics; Preliminary test estimator; Symmetry model; Marginal homogeneity; Contingency-tables
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:17332
References:

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