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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Eskandari, F., Meshkani, M. Empirical Bayes analysis of log-linear models for a generalized finite stationary Markov chain. Metrika 59, 173–191 (2004). https://doi.org/10.1007/s001840300278
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DOI: https://doi.org/10.1007/s001840300278