Empirical Bayes analysis of log-linear models for a generalized finite stationary Markov chain |
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Authors: | Farzad?Eskandari mailto:f-eskandari@cc.sbu.ac.ir" title=" f-eskandari@cc.sbu.ac.ir" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Mohammad R.?Meshkani |
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Affiliation: | (1) Department of Statistics, Allameh Tabatabaee University, Tehran, 16565, Iran;(2) Department of Statistics, Shahid Beheshti University, Tehran, 19838, Iran |
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Abstract: | This article presents the empirical Bayes method for estimation of the transition probabilities of a generalized finite stationary Markov chain whose ith state is a multi-way contingency table. We use a log-linear model to describe the relationship between factors in each state. The prior knowledge about the main effects and interactions will be described by a conjugate prior. Following the Bayesian paradigm, the Bayes and empirical Bayes estimators relative to various loss functions are obtained. These procedures are illustrated by a real example. Finally, asymptotic normality of the empirical Bayes estimators are established. |
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Keywords: | Log-linear models Multinomial distribution Finite stationary Markov chain Bayes Empirical Bayes Model Selection Panel data |
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