Ziv-Merhav estimation for hidden-Markov processes
Nicholas Barnfield, Rapha\"el Grondin, Gaia Pozzoli, Renaud Raqu\'epas
TL;DR
This paper proves the strong consistency of a Ziv-Merhav-type estimator for the cross entropy rate in hidden-Markov processes, employing novel decoupling and thermodynamic formalism techniques.
Contribution
It introduces a new proof strategy for estimator consistency, focusing on decoupling properties and thermodynamic formalism in hidden-Markov processes.
Findings
Proves strong consistency of the estimator.
Employs novel proof techniques involving decoupling.
Utilizes thermodynamic formalism tools.
Abstract
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.
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