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Entropy 2013, 15(6), 1999-2011; doi:10.3390/e15061999

Bias Adjustment for a Nonparametric Entropy Estimator

*  and
Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, NC 28223, USA
* Author to whom correspondence should be addressed.
Received: 20 March 2013 / Revised: 8 May 2013 / Accepted: 17 May 2013 / Published: 23 May 2013
(This article belongs to the Special Issue Estimating Information-Theoretic Quantities from Data)
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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.
Keywords: nonparametric entropy estimation; bias nonparametric entropy estimation; bias
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhang, Z.; Grabchak, M. Bias Adjustment for a Nonparametric Entropy Estimator. Entropy 2013, 15, 1999-2011.

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