Geodesic
Maximum likelihood estimator and Kullback--Leibler information in misspecified Markov chain models
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 169-178

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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: Kullback–Leibler information, maximum likelihood estimator, incorrect model.
Mots-clés : efficient estimation, Markov chain 
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     author = {P. E. Greenwood and W. Wefelmeyer},
     title = {Maximum likelihood estimator and {Kullback--Leibler} information in misspecified {Markov} chain models},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a10/}
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P. E. Greenwood; W. Wefelmeyer. Maximum likelihood estimator and Kullback--Leibler information in misspecified Markov chain models. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 169-178. http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a10/