A GENERAL THEORY OF PARTICLE FILTERS IN HIDDEN MARKOV MODELS AND SOME APPLICATIONS

• 成果类型: Article
• 署名作者: Chan, Hock Peng; Lai, Tze Leung
• 署名单位: National University of Singapore; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1172
• 发表日期: 2013
• 页码: 2877-2904
• 关键词: monte-carlo methods

摘要

By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated dependence among the sample paths, the asymptotic variance formula and martingale representations lead to consistent estimates of the standard errors of the particle filter estimates of the hidden states.