Juan A Bonachela et al 2008 J. Phys. A: Math. Theor. 41 202001 doi:10.1088/1751-8113/41/20/202001
Entropy estimates of small data sets
FREE ARTICLEJuan A Bonachela1,2, Haye Hinrichsen2 and Miguel A Muñoz1
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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.
- PACS
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05.70.Ce Thermodynamic functions and equations of state
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
- MSC
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94A17 Measures of information, entropy
82B30 Statistical thermodynamics (See also 80-XX)
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
- Subjects
- Dates
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Issue 20 (23 May 2008)
Received 21 December 2007, in final form 10 April 2008
Published 29 April 2008
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Entropy estimates of small data sets
Juan A Bonachela et al 2008 J. Phys. A: Math. Theor. 41 202001
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