Abstract
A problem of improving the accuracy of nonparametric entropy estimationfor 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 metricsand 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 Cramér-Rao lower bound.
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