Nearest-neighbor Entropy Estimators with Weak Metrics

Evgeniy Timofeev; Alexei Kaltchenko

doi:10.3934/amc.2014.8.119

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arXiv · 1205.5856

Nearest-neighbor Entropy Estimators with Weak Metrics

Evgeniy Timofeev·Alexei Kaltchenko

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Abstract

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. Based on weak metrics, a new nearest-neighbor entropy estimator is constructed 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.

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BibTeX RIS

Evgeniy Timofeev, Alexei Kaltchenko. 2012-05-26. Nearest-neighbor Entropy Estimators with Weak Metrics. https://doi.org/10.3934/amc.2014.8.119

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