Ziv-Merhav Estimation for Hidden-Markov Processes
Nicholas Barnfield, Raphael Grondin, Gaia Pozzoli, Renaud Raquépas · 2024
We present a proof of strong consistency of a Ziv-Merhav-type estimator of the cross entropy rate for pairs of hidden-Markov processes. Our proof strategy has two novel aspects: the focus on decoupling properties of the laws and the use of tools from the thermodynamic formalism.