This article is cited in 4 papers

Selection of a metric for the nearest neighbor entropy estimators

E. A. Timofeev

P. G. Demidov Yaroslavl State University, Yaroslavl, Russia

Abstract: We consider the problem of improving the efficiency of the nonparametric entropy estimation for a stationary ergodic process. Our approach is based on the nearest-neighbor distances. We propose a broad class of metrics on the space of right-sided infinite sequences drawn from a finite alphabet. The new metric has a parameter which is a nonincreasing function. We prove that, under certain conditions, our estimators have a small variance and show that a special selection of the metric parameters reduces the estimator's bias.

UDC: 519.72+519.234

 English version: Journal of Mathematical Sciences (New York), 2014, 203:6, 892–906

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