Nemenman, 2011b

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I Nemenman. Coincidences and estimation of entropies of random variables with large cardinalities. Entropy 13, 2013-2023, 2011. PDF, arXiv.

Abstract

We perform an asymptotic analysis of the NSB estimator of entropy of a discrete random variable. The analysis illuminates the dependence of the estimates on the number of coincidences in the sample and shows that the estimator has a well defined limit for a large cardinality of the studied variable. This allows estimation of entropy with no a priori assumptions about the cardinality. Software implementation of the algorithm is available.