FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 2, PAGES 209-227

**Selection of a metric for the nearest neighbor entropy estimators**

E. A. Timofeev

Abstract

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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.

Location: http://mech.math.msu.su/~fpm/eng/k13/k132/k13217h.htm

Last modified: January 7, 2014