Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models

Randal Douc; Eric Moulines

doi:10.1214/12-AOS1047

Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models

CNRS LTCI

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Abstract

Let (Y_k)_k∈Z be a stationary sequence on a probability space (Ω,A,P) taking values in a standard Borel space Y. Consider the associated maximum likelihood estimator with respect to a parametrized family of hidden Markov models such that the law of the observations (Y_k)_k∈Z is not assumed to be described by any of the hidden Markov models of this family. In this paper we investigate the consistency of this estimator in such misspecified models under mild assumptions.

Original language	English
Pages (from-to)	2697-2732
Number of pages	36
Journal	Annals of Statistics
Volume	40
Issue number	5
DOIs	https://doi.org/10.1214/12-AOS1047
Publication status	Published - 1 Oct 2012

Keywords

Hidden Markov models
Maximum likelihood estimator
Misspecified models
State space models
Strong consistency

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10.1214/12-AOS1047

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abstract = "Let (Yk)k∈Z be a stationary sequence on a probability space (Ω,A,P) taking values in a standard Borel space Y. Consider the associated maximum likelihood estimator with respect to a parametrized family of hidden Markov models such that the law of the observations (Yk)k∈Z is not assumed to be described by any of the hidden Markov models of this family. In this paper we investigate the consistency of this estimator in such misspecified models under mild assumptions.",

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AB - Let (Yk)k∈Z be a stationary sequence on a probability space (Ω,A,P) taking values in a standard Borel space Y. Consider the associated maximum likelihood estimator with respect to a parametrized family of hidden Markov models such that the law of the observations (Yk)k∈Z is not assumed to be described by any of the hidden Markov models of this family. In this paper we investigate the consistency of this estimator in such misspecified models under mild assumptions.

KW - Hidden Markov models

KW - Maximum likelihood estimator

KW - Misspecified models

KW - State space models

KW - Strong consistency

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Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models

Abstract

Keywords

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