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Nearest-neighbor Entropy Estimators with Weak Metrics (1205.5856v1)
Published 26 May 2012 in cs.IT, math.IT, math.ST, and stat.TH
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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