Efficiency of Empirical Estimators for Markov Chains
P. E. Greenwood, W. Wefelmeyer
The Annals of Statistics · 1995 · Volume 23 · Issue 1
Abstract
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.
Keywords
62G20; 62M05; efficiency; empirical estimator; Markov chain;
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