This article is cited in 8 papers

Maximum likelihood estimator and Kullback–Leibler information in misspecified Markov chain models

P. E. Greenwood^a, W. Wefelmeyer<sup>b

a</sup> University of British Columbia
^b University of Siegen

Abstract: Suppose we have specified a parametric model for the transition distribution of a Markov chain, but the true transition distribution does not belong to the model. Then the maximum likelihood estimator estimates the parameter which maximizes the Kullback–Leibler information between the true transition distribution and the model. We prove that the maximum likelihood estimator is asymptotically efficient in a nonparametric sense if the true transition distribution is unknown.

Keywords: efficient estimation, Kullback–Leibler information, Markov chain, maximum likelihood estimator, incorrect model.

Received: 31.10.1995

Language: English

DOI: 10.4213/tvp1718

 English version: Theory of Probability and its Applications, 1998, 42:1, 103–111

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