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.
@article{1176324459,
author = {Greenwood, P. E. and Wefelmeyer, W.},
title = {Efficiency of Empirical Estimators for Markov Chains},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 132-143},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324459}
}
Greenwood, P. E.; Wefelmeyer, W. Efficiency of Empirical Estimators for Markov Chains. Ann. Statist., Tome 23 (1995) no. 6, pp. 132-143. http://gdmltest.u-ga.fr/item/1176324459/