ADAPTIVE ESTIMATION OF A DENSITY FUNCTION USING BETA KERNELS

被引：7

作者：

Bertin, Karine ^{[1
]}

Klutchnikoff, Nicolas ^{[2
,3
,4
]}

机构：

[1] Univ Valparaiso, CIMFAV, Valparaiso 2421, Chile

[2] Univ Strasbourg, CREST ENSAI, F-35172 Bruz, France

[3] Univ Strasbourg, IRMA, UMR 7501, F-35172 Bruz, France

[4] CNRS, F-35172 Bruz, France

来源：

ESAIM-PROBABILITY AND STATISTICS | 2014年 / 18卷

关键词：

Beta kernels; adaptive estimation; minimax rates; Holder spaces; END-POINTS;

D O I：

10.1051/ps/2014010

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we are interested in the estimation of a density - defined on a compact interval of R - from n independent and identically distributed observations. In order to avoid boundary effect, beta kernel estimators are used and we propose a procedure (inspired by Lepski's method) in order to select the bandwidth. Our procedure is proved to be adaptive in an asymptotically minimax framework. Our estimator is compared with both the cross-validation algorithm and the oracle estimator using simulated data.

引用

页码：400 / 417

页数：18

共 25 条

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Abdous B., 2009, African Diaspora Journal of Mathematics, V8, P63

[2]

[Anonymous], MONOGR STAT APPL PRO

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