NEAREST-NEIGHBOR ENTROPY ESTIMATORS WITH WEAK METRICS

被引：1

作者：

Timofeev, Evgeniy ^{[1
]}

Kaltchenko, Alexei ^{[2
]}

机构：

[1] Yaroslavl State Univ, Dept Comp Sci, Yaroslavl, Russia

[2] Wilfrid Laurier Univ, Dept Phys & Comp Sci, Waterloo, ON N2L 3C5, Canada

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2014年 / 8卷 / 02期

关键词：

Entropy; stochastic process; stationary; estimation; nonparametric; nearest neighbor; bias; metric; CONVERGENCE; SEQUENCES;

D O I：

10.3934/amc.2014.8.119

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. A new nonparametric entropy estimator is constructed based on weak metrics and has a parameter with which the estimator is optimized to reduce its bias. It is shown that estimator's variance is upper-bounded by a nearly optimal Cramer-Rao lower bound.

引用

页码：119 / 127

页数：9

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