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Preprints, Working Papers, ... Year : 2009

Consistency of the Maximum Likelihood Estimator for general hidden Markov models

Abstract

Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is strongly consistent under a rather minimal set of assumptions. As special cases of our main result, we obtain consistency in a large class of nonlinear state space models, as well as general results on linear Gaussian state space models and finite state models. A novel aspect of our approach is an information-theoretic technique for proving identifiability, which does not require an explicit representation for the relative entropy rate. Our method of proof could therefore form a foundation for the investigation of MLE consistency in more general dependent and non-Markovian time series. Also of independent interest is a general concentration inequality for $V$-uniformly ergodic Markov chains.
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Dates and versions

hal-00442774 , version 1 (22-12-2009)

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Randal Douc, Eric Moulines, Jimmy Olsson, Ramon van Handel. Consistency of the Maximum Likelihood Estimator for general hidden Markov models. 2009. ⟨hal-00442774⟩
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