Bernoulli

  • Bernoulli
  • Volume 5, Number 1 (1999), 109-123.

Reversible Markov chains and optimality of symmetrized empirical estimators

Priscilla E. Greenwood and Wolfgang Wefelmeyer

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Abstract

Suppose that we want to estimate the expectation of a function of two arguments under the stationary distribution of two successive observations of a reversible Markov chain. Then the usual empirical estimator can be improved by symmetrizing. We show that the symmetrized estimator is efficient. We point out applications to discretely observed continuous-time processes. The proof is based on a result for general Markov chain models which can be used to characterize efficient estimators in any model defined by restrictions on the stationary distribution of a single or two successive observations.

Article information

Source
Bernoulli, Volume 5, Number 1 (1999), 109-123.

Dates
First available in Project Euclid: 12 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1173707097

Mathematical Reviews number (MathSciNet)
MR1673568

Zentralblatt MATH identifier
0958.62076

Keywords
discretely observed diffusions efficient estimation inference for stochastic processes martingale approximation

Citation

Greenwood, Priscilla E.; Wefelmeyer, Wolfgang. Reversible Markov chains and optimality of symmetrized empirical estimators. Bernoulli 5 (1999), no. 1, 109--123. https://projecteuclid.org/euclid.bj/1173707097


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