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Zbl 0822.62067
Greenwood, P.E.; Wefelmeyer, W.
Efficiency of empirical estimators for Markov chains. (English)
[J] Ann. Stat. 23, No.1, 132-143 (1995). ISSN 0090-5364

Summary: Suppose we observe a uniformly ergodic Markov chain with unknown transition distribution. The empirical estimator for a linear functional of the (invariant) joint distribution of two successive observations is defined using the pairs of successive observations. Its efficiency is proved using a martingale approximation. As a corollary we show efficiency of the empirical joint distribution function in the sense of a functional convolution theorem.

MSC 2000:: *62M05 Markov processes: estimation
62G30 Order statistics, etc.

Keywords: empirical distribution; uniformly ergodic Markov chain; unknown transition distribution; empirical estimator; linear functional; efficiency; martingale approximation; empirical joint distribution function; functional convolution theorem

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