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Estimating the variance of Shannon entropy.
Ricci, Leonardo; Perinelli, Alessio; Castelluzzo, Michele.
Afiliação
  • Ricci L; Department of Physics, University of Trento, 38123 Trento, Italy.
  • Perinelli A; CIMeC, Center for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy.
  • Castelluzzo M; CIMeC, Center for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy.
Phys Rev E ; 104(2-1): 024220, 2021 Aug.
Article em En | MEDLINE | ID: mdl-34525589
ABSTRACT
The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly the most widespread tool is provided by the so-called plug-in estimator, whose statistical properties in terms of bias and variance were investigated since the first decade after the publication of Shannon's seminal works. In the case of an underlying multinomial distribution, while the bias can be evaluated by knowing support and data set size, variance is far more elusive. The aim of the present work is to investigate, in the multinomial case, the statistical properties of an estimator of a parameter that describes the variance of the plug-in estimator of Shannon entropy. We then exactly determine the probability distributions that maximize that parameter. The results presented here allow one to set upper limits to the uncertainty of entropy assessments under the hypothesis of memoryless underlying stochastic processes.

Texto completo: 1 Base de dados: MEDLINE Idioma: En Revista: Phys Rev E Ano de publicação: 2021 Tipo de documento: Article País de afiliação: Itália

Texto completo: 1 Base de dados: MEDLINE Idioma: En Revista: Phys Rev E Ano de publicação: 2021 Tipo de documento: Article País de afiliação: Itália