Algorithm for Efficient Entropy Estimation

We consider the problem of the nonparametric entropy estimation of a stationary ergodic process. Our approach is based on the nearest-neighbor distances. We propose a broad class of metrics on the space $\Omega = A^{\mathbb{N}}$ of right-sided infinite sequences drawn from a finite alphabet $A$. The new metric has a parameter which is a non-increasing function. We apply this metrics to nearest-neighbor entropy estimators. We prove that, under certain conditions, the estimators has a small variance. We show that a special selection of the metric parameters reduction of the estimator's bias. The article is published in the author's wording.