Title: Consistency of Maximum Likelihood Parameter Estimation for Bivariate Markov Chains
Abstract: Abstract A bivariate Markov chain comprises a pair of random processes which are jointly, but not necessarily individually, Markov. We are interested in continuous-time finite-alphabet bivariate Markov chains. Only one of the two processes of the bivariate Markov chain is observable. The observable process, and the other underlying process, may jump simultaneously. Examples of bivariate Markov chains include the Markov modulated Poisson process, and the batch Markovian arrival process, when suitable modulo counts are applied. An Expectation-Maximization (EM) algorithm for maximum likelihood estimation of the parameter of a bivariate Markov chain was recently developed. Here we prove strong consistency of maximum likelihood parameter estimation for the bivariate Markov chain. We extend the proofs developed by Leroux for hidden Markov processes and by Rydén for Markov modulated Poisson processes, to bivariate Markov chains. Such chains do not generally have a hidden Markov process representation. Keywords: Bivariate Markov chainConsistencyMaximum likelihoodMathematics Subject Classification: Primary 62M05Secondary 62F12 ACKNOWLEDGMENTS This work was supported in part by the U.S. National Science Foundation under grant CCF-0916568. The authors thank Tobias Rydén for taking the time to read the manuscript and for his valuable comments. The first author thanks Amir Dembo for useful discussions and comments. The authors thank Neri Merhav and the anonymous referees for critical reading of the manuscript and their useful comments, which helped improve the presentation of this work.
Publication Year: 2013
Publication Date: 2013-02-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 4
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