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arXiv · 1602.07440

On the Kozachenko-Leonenko entropy estimator

Nicolas Fournier·Sylvain Delattre
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Abstract

We study in details the bias and variance of the entropy estimator proposed by Kozachenko and Leonenko for a large class of densities on $\mathbb{R}^d$. We then use the work of Bickel and Breiman to prove a central limit theorem in dimensions $1$ and $2$. In higher dimensions, we provide a development of the bias in terms of powers of $N^{-2/d}$. This allows us to use a Richardson extrapolation to build, in any dimension, an estimator satisfying a central limit theorem and for which we can give some some explicit (asymptotic) confidence intervals.

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Nicolas Fournier, Sylvain Delattre. 2016-02-24. On the Kozachenko-Leonenko entropy estimator. https://arxiv.org/abs/1602.07440

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