INFORMATION GEOMETRY APPROACH TO PARAMETER ESTIMATION IN MARKOV CHAINS

• 成果类型: Article
• 署名作者: Hayashi, Masahito; Watanabe, Shun
• 署名单位: Nagoya University; National University of Singapore; Tokyo University of Agriculture & Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1420
• 发表日期: 2016
• 页码: 1495-1535
• 关键词: exponential-families; monte-carlo; STOCHASTIC-PROCESSES; bounds; error; mcmc; THEOREM

摘要

We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then we show that the sample mean of the generator of the exponential family is an asymptotically efficient estimator. Further, we also define a curved exponential family of transition matrices. Using a transition matrix version of the Pythagorean theorem, we give an asymptotically efficient estimator for a curved exponential family.