Bias adjustment for a nonparametric entropy estimator

Abstract

Zhang in 2012 introduced a nonparametric estimator of Shannon's entropy, whose bias decays exponentially fast when the alphabet is finite. We propose a methodology to estimate the bias of this estimator. We then use it to construct a new estimator of entropy. Simulation results suggest that this bias adjusted estimator has a significantly lower bias than many other commonly used estimators. We consider both the case when the alphabet is finite and when it is countably infinite. © 2013 by the authors; licensee MDPI, Basel, Switzerland.