Universal pointwise selection rule in multivariate function estimation

被引：45

作者：

Goldenshluger, Alexander ^{[1
]}

Lepski, Oleg ^{[2
]}

机构：

[1] Univ Haifa, Dept Stat, IL-31905 Haifa, Israel

[2] Univ Aix Marseille 1, Lab Anal Topol & Probabil, CNRS, UMR 6632, F-13453 Marseille, France

来源：

BERNOULLI | 2008年 / 14卷 / 04期

关键词：

adaptive estimation; minimax risk; optimal rates of convergence; pointwise estimation;

D O I：

10.3150/08-BEJ144

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 study the problem of pointwise estimation of a multivariate function. We develop a general pointwise estimation procedure that is based on selection of estimators from a large parameterized collection. An upper bound on the pointwise risk is established and it is shown that the proposed selection procedure specialized for different collections of estimators leads to minimax and adaptive minimax estimators in various settings.

引用

页码：1150 / 1190

页数：41

共 22 条

[1]

Adler R. J., 2007, Springer Monographs in Mathematics

[2] Asymptotically exact minimax estimation in sup-norm for anisotropic Holder classes [J].