EFFICIENT MULTIVARIATE ENTROPY ESTIMATION VIA k-NEAREST NEIGHBOUR DISTANCES
EFFICIENT MULTIVARIATE ENTROPY ESTIMATION VIA k-NEAREST NEIGHBOUR DISTANCES
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DOI：
10.1214/18-aos1688
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发表时间：
2019-02-01
影响因子：
4.5
通讯作者：
Yuan, Ming
中科院分区：
文献类型：
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作者：
Berrett, Thomas B.;Samworth, Richard J.;Yuan, Ming
许多统计程序，包括拟合优度检验和独立成分分析方法，都严重依赖于对分布熵的估计。在本文中，我们寻求熵估计，是有效的，并达到当地的渐近极小极大下界平方误差损失。为此，我们研究加权平均的估计最初提出的Kozachenko和Leonenko [问题。传输23（1987），95-101]，基于R-d中n个独立且同分布的随机向量的样本的k-最近邻距离。仔细选择权重使我们能够在任意维度上获得有效的估计，给定足够的光滑性，而原始的未加权估计通常仅在d
Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient and achieve the local asymptotic minimax lower bound with respect to squared error loss. To this end, we study weighted averages of the estimators originally proposed by Kozachenko and Leonenko [Probl. Inform. Transm. 23 (1987), 95-101], based on the k-nearest neighbour distances of a sample of n independent and identically distributed random vectors in R-d. A careful choice of weights enables us to obtain an efficient estimator in arbitrary dimensions, given sufficient smoothness, while the original unweighted estimator is typically only efficient when d