Maximum Likelihood Estimator and Kullback--Leibler Information in Misspecified Markov Chain Models
Priscilla E. Greenwood, Wolfgang Wefelmeyer · Theory of Probability and Its Applications · 1998
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.