Concentration of empirical entropy and transfer entropy for non-regular chains with unbounded memory
José O. Santana, Ricardo F. Ferreira
Source abstract
We study plug-in estimators of the entropy rate and the transfer entropy rate for stationary finite-alphabet chains with unbounded memory. Under a coalescent coupling-from-the-past assumption, we establish non-asymptotic concentration inequalities around the expectations of the estimators. Under additional uniform non-nullness and exponential beta-mixing assumptions, we control the corresponding biases and obtain concentration around the entropy and transfer entropy rates, together with almost-sure consistency. The results apply to chains governed by g-functions that need not be globally continuous.
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