On the Kozachenko-Leonenko entropy estimator
On the Kozachenko-Leonenko entropy estimator
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DOI：
10.1016/j.jspi.2017.01.004
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发表时间：
2017-06-01
影响因子：
0.9
通讯作者：
Fournier, Nicolas
中科院分区：
文献类型：
--
作者：
Delattre, Sylvain;Fournier, Nicolas
We study in detail the bias and variance of the entropy estimator proposed by Kozachenko and Leonenko (1987) for a large class of densities on R-d. We then use the work of Bickel and Breiman (1983) 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, a root-n consistent entropy estimator satisfying a central limit theorem which allows for explicit (asymptotic) confidence intervals. To our knowledge, all the previous general root-n consistency results were concerning dimension 1. (C) 2017 Elsevier B.V. All rights reserved.
