The asymptotic minimax constant for sup-norm loss in nonparametric density estimation

被引：16

作者：

Korostelev, A ^{[1
]}

Nussbaum, M

机构：

[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[2] Karl Weierstrass Inst Math, D-10117 Berlin, Germany

来源：

BERNOULLI | 1999年 / 5卷 / 06期

关键词：

density estimation; exact constant; optimal recovery; uniform norm risk; white noise;

D O I：

10.2307/3318561

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：

We develop the exact constant of the risk asymptotics in the uniform norm for density estimation. This constant has already been found for nonparametric regression and for signal estimation in Gaussian white noise. Holder classes for arbitrary smoothness index beta>0 on the unit interval are considered. The constant involves the value of an optimal recovery problem as in the white noise case, but in addition it depends on the maximum of densities in the function class.

引用

页码：1099 / 1118

页数：20

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