THE MAXIMIZING SET OF THE ASYMPTOTIC NORMALIZED LOG-LIKELIHOOD FOR PARTIALLY OBSERVED MARKOV CHAINS

• 成果类型: Article
• 署名作者: Douc, Randal; Roueff, Francois; Sim, Tepmony
• 署名单位: Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1149
• 发表日期: 2016
• 页码: 2357-2383
• 关键词: time-series; models; estimator; CONVERGENCE; Consistency; ergodicity; rates

摘要

This paper deals with a parametrized family of partially observed bivariate Markov chains. We establish that, under very mild assumptions, the limit of the normalized log-likelihood function is maximized when the parameters belong to the equivalence class of the true parameter, which is a key feature for obtaining the consistency of the maximum likelihood estimators (MLEs) in well-specified models. This result is obtained in the general framework of partially dominated models. We examine two specific cases of interest, namely, hidden Markov models (HMMs) and observation-driven time series models. In contrast with previous approaches, the identifiability is addressed by relying on the uniqueness of the invariant distribution of the Markov chain associated to the complete data, regardless its rate of convergence to the equilibrium.