Comparative Construction of Plug-in Estimators of the Entropy Rate of Two-state Markov Chains

摘要

The entropy rate of an ergodic homogeneous Markov chain taking only two values is an explicit function of its transition probabilities. We study plug-in estimators of this entropy rate based on the observation of either one trajectory with long length or several trajectories with fixed length. Their exact asymptotic distributions are given. A detailed numerical study using simulation results is provided. Real data of rainfall occurrences are studied.