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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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) , Ireland et al. (1969) , Quade and Salama (1975)  Cressie and Read (1988) , Menendez et al. (2005) ) 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)  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.
|Uncontrolled Keywords:||Minimum phi-divergence estimator; Phi-divergence statistics; Preliminary test estimator; Symmetry model; Marginal homogeneity; Contingency-tables|
|Subjects:||Sciences > Mathematics > Mathematical statistics|
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|Deposited On:||05 Dec 2012 10:18|
|Last Modified:||05 Dec 2012 18:47|