Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models

• 成果类型: Article
• 署名作者: Bickel, PJ; Ritov, Y; Rydén, T
• 署名单位: University of California System; University of California Berkeley; Lund University; Hebrew University of Jerusalem
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1614-1635
• 关键词: em algorithm; seizure counts; Mixture Model; time-series

摘要

Hidden Markov models (HMMs) have during the last decade become a widespread tool for modeling sequences of dependent random variables. Inference for such models is usually based on the maximum-likelihood estimator (MLE), and consistency of the MLE for general HMMs was recently proved by Leroux. In this paper me show that under mild conditions the MLE is also asymptotically normal and prove that the observed information matrix is a consistent estimator of the Fisher information.