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Empirical Bayes analysis of log-linear models for a generalized finite stationary Markov chain
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
Affiliation:(1) Department of Statistics, Allameh Tabatabaee University, Tehran, 16565, Iran;(2) Department of Statistics, Shahid Beheshti University, Tehran, 19838, Iran
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.
Keywords:Log-linear models  Multinomial distribution  Finite stationary Markov chain  Bayes  Empirical Bayes  Model Selection  Panel data
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