Geodesic
Algorithm for Efficient Entropy Estimation
Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 2, pp. 178-185.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the problem of the nonparametric entropy estimation of a stationary ergodic process. Our approach is based on the nearest-neighbor distances. We propose a broad class of metrics on the space $\Omega = A^{\mathbb{N}}$ of right-sided infinite sequences drawn from a finite alphabet $A$. The new metric has a parameter which is a non-increasing function. We apply this metrics to nearest-neighbor entropy estimators. We prove that, under certain conditions, the estimators has a small variance. We show that a special selection of the metric parameters reduction of the estimator's bias. The article is published in the author's wording.
Keywords: entropy, nonparametric statistic, metric, ball, Bernoulli’s measure. 
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E. A. Timofeev. Algorithm for Efficient Entropy Estimation. Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 2, pp. 178-185. http://geodesic.mathdoc.fr/item/MAIS_2013_20_2_a13/

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