CONSISTENCY OF THE MAXIMUM LIKELIHOOD ESTIMATOR FOR GENERAL HIDDEN MARKOV MODELS

• 成果类型: Article
• 署名作者: Douc, Randal; Moulines, Eric; Olsson, Jimmy; van Handel, Ramon
• 署名单位: IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Lund University; Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS834
• 发表日期: 2011
• 页码: 474-513
• 关键词: probabilistic functions; geometric ergodicity; INEQUALITY; chains

摘要

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.