Consistent Estimation of the Order for Markov and Hidden Markov Chains

Abstract

The structural parameters of many statistical models can be estimated by maximizing a penalized version of the likelihood function. The author uses this idea to construct strongly consistent estimators of the order for Markov Chain and Hidden Markov Chain models. The specification of the penalty term requires precise information on the rate of growth of the maximized likelihood ratio. For Markov Chain models, he determines the rate using the Law of the Iterated Logarithm. For Hidden Markov Chain models, he finds an upper bound to the rate using results from Information Theory. He gives sufficient conditions on the penalty term to avoid overestimation and underestimation of the order. Examples of penalty terms that generate strongly consistent estimators also are given.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1990
Accession Number
ADA452001

Entities

People

  • Lorenzo Finesso

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Availability
  • Classification
  • Contracts
  • Engineering
  • Estimators
  • Information Operations
  • Information Theory
  • Instructions
  • Markov Chains
  • Maryland
  • Mathematics
  • Monitoring
  • Specifications
  • Standards
  • Universities

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Statistical inference.