EFFICIENCY OF EMPIRICAL ESTIMATORS FOR MARKOV-CHAINS

Suppose we observe a uniformly ergodic Markov chain with unknown trans ition 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 effici ency of the empirical joint distribution function in the sense of a fu nctional convolution theorem.