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

Peter J. Bickel*, Ya'acov Ritov, Tobias Rydén

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

207 Scopus citations

Abstract

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 we 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.

Original languageEnglish
Pages (from-to)1614-1635
Number of pages22
JournalAnnals of Statistics
Volume26
Issue number4
DOIs
StatePublished - Aug 1998

Keywords

  • Asymptotic normality
  • Hidden Markov model
  • Incomplete data
  • Missing data

Fingerprint

Dive into the research topics of 'Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models'. Together they form a unique fingerprint.

Cite this