Statistical Estimation of the Shannon Entropy

查看全文 作　　者：Alexander [1]BULINSKI;Denis [1]DIMITROV

机构地区：[1]Steklov Mathematical Institute of Russian Academy of Sciences and Department of Mathematics and Mechanics,Lomonosov Moscow State University,Moscow 119234,Russia

出　　处：《Acta Mathematica Sinica,English Series》索引2019年第35卷第1期,共30页

基　　金：Supported by the Russian Science Foundation(Grant No.14-21-00162) 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 L^2-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. 关键词：Shannon differential entropy Kozachenko-Leonenko estimates HARDY-LITTLEWOOD maxi-mal function ANALOGUES ASYMPTOTIC UNBIASEDNESS and L^2-consistency Gaussian VECTORS

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Statistical Estimation of the Shannon Entropy

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