Entropy estimates of small data sets

by: Juan A Bonachela, Haye Hinrichsen, Miguel A Munoz

(29 Apr 2008)

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arXiv (abstract), arXiv (PDF)

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Abstract

Estimating entropies from limited data series is known to be a non-trivial task. Naive 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 out-performs 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.

@misc{citeulike:2742234, abstract = {Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon, R\'enyi and Tsallis) specially devised to provide a compromise between low bias and small statistical errors, for short data series. This new estimator out-performs 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.}, author = {Bonachela, Juan A. and Hinrichsen, Haye and Munoz, Miguel A. }, citeulike-article-id = {2742234}, eprint = {0804.4561}, keywords = {entropy, statistics}, month = {Apr}, posted-at = {2008-05-11 08:23:46}, priority = {2}, title = {Entropy estimates of small data sets}, url = {http://arxiv.org/abs/0804.4561}, year = {2008} }

RIS record

TY - ELEC ID - citeulike:2742234 L3 - citeulike-article-id:2742234 TI - Entropy estimates of small data sets N2 - Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon, R\'enyi and Tsallis) specially devised to provide a compromise between low bias and small statistical errors, for short data series. This new estimator out-performs 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. KW - entropy KW - statistics AU - Bonachela, Juan AU - Hinrichsen, Haye AU - Munoz, Miguel PY - 2008/Apr/29/ UR - http://arxiv.org/abs/0804.4561 ER -

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