Second-Order Moments of a Stationary Markov Chain and Some Applications

Abstract

The i-th state of a finite-state Markov chain can be indicated by a vector with 1 in the i-th position and O's in the other positions. The vector-valued process defined in this way is autoregressive in the wide sense. The second-order moments, moving average representation, and spectral density of this process are obtained. The numerical-valued chain is a linear function of the vector; a simple condition is derived for it to be first-order autoregressive in the wide sense. The stationary probabilities of the chain can be estimated by the means of observations on the vector-valued process; this estimator is asymptotically equivalent to the maximum likelihood estimator.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1989
Accession Number
ADA206366

Entities

People

  • Theodore W. Anderson

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Computational Science
  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Markov Chains
  • Markov Processes
  • Observation
  • Probability
  • Random Variables
  • Stationary
  • Stationary Processes
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Statistical inference.