CONSISTENCY OF MAXIMUM LIKELIHOOD ESTIMATION FOR SOME DYNAMICAL SYSTEMS

• 成果类型: Article
• 署名作者: McGoff, Kevin; Mukherjee, Sayan; Nobel, Andrew; Pillai, Natesh
• 署名单位: Duke University; Duke University; Duke University; University of North Carolina; University of North Carolina Chapel Hill; Harvard University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1259
• 发表日期: 2015
• 页码: 1-29
• 关键词: statistical stability; probabilistic functions; asymptotic properties; Markov; inference; normality; models

摘要

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures.