Statistical Estimation of the Shannon Entropy

被引：3

作者：

Alexander BULINSKI ^{[1
]}

Denis DIMITROV ^{[2
]}

机构：

[1] Steklov Mathematical Institute of Russian Academy of Sciences

[2] Department of Mathematics and Mechanics,Lomonosov Moscow State University

来源：

ActaMathematicaSinica | 2019年 / 35卷 / 01期

关键词：

D O I：

暂无

中图分类号：

O414.11 [基本定律];

学科分类号：

080701 ;

摘要：

The behavior of the Kozachenko–Leonenko estimates for the（differential） Shannon entropy is studied when the number of i.i.d. vector-valued observations tends to infinity. The asymptotic unbiasedness and L2-consistency of the estimates are established. The conditions employed involve the analogues of the Hardy–Littlewood maximal function. It is shown that the results are valid in particular for the entropy estimation of any nondegenerate Gaussian vector.

引用

页码：17 / 46

页数：30

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