ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATION IN MISSPECIFIED HIDDEN MARKOV MODELS

• 成果类型: Article
• 署名作者: Douc, Randal; Moulines, Eric
• 署名单位: IMT - Institut Mines-Telecom; IMT Atlantique; Institut Polytechnique de Paris; Telecom SudParis; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT Atlantique
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1047
• 发表日期: 2012
• 页码: 2697-2732
• 关键词: probabilistic functions; filters

摘要

Let (Y-k)(k is an element of Z) be a stationary sequence on a probability space (Omega, 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 is an element of 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.