Article ID Journal Published Year Pages File Type
1149575 Journal of Statistical Planning and Inference 2009 12 Pages PDF
Abstract

This article concerns the variance estimation in the central limit theorem for finite recurrent Markov chains. The associated variance is calculated in terms of the transition matrix of the Markov chain. We prove the equivalence of different matrix forms representing this variance. The maximum likelihood estimator for this variance is constructed and it is proved that it is strongly consistent and asymptotically normal. The main part of our analysis consists in presenting closed matrix forms for this new variance. Additionally, we prove the asymptotic equivalence between the empirical and the maximum likelihood estimation (MLE) for the stationary distribution.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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