Nearest-neighbor Entropy Estimators with Weak Metrics
Information Theory
2024-11-04 v1 math.IT
Statistics Theory
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1205.5856,
title = {Nearest-neighbor Entropy Estimators with Weak Metrics},
author = {Evgeniy Timofeev and Alexei Kaltchenko},
journal= {arXiv preprint arXiv:1205.5856},
year = {2024}
}
Comments
9 pages, no figures