Entropy estimates of small data sets

Bonachela, Juan A. and Hinrichsen, Haye and Muñoz, Miguel A. (2008) Entropy estimates of small data sets. Journal of Physics A: Mathematical and Theoretical, 41 (20). ISSN 1751-8113

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Abstract

Estimating entropies from limited data series is known to be a non-trivial task. Naïve estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals (Shannon, Rényi and Tsallis) specially devised to provide a compromise between low bias and small statistical errors, for short data series. This new estimator outperforms other currently available ones when the data sets are small and the probabilities of the possible outputs of the random variable are not close to zero. Otherwise, other well-known estimators remain a better choice. The potential range of applicability of this estimator is quite broad specially for biological and digital data series.