Regression with random design: A minimax study

被引：17

作者：

Chesneau, Christophe ^{[1
]}

机构：

[1] Univ Paris 06, CNRS UMR 7599, Lab Probabill & Modeles Aleatoires, UFR Math, F-75013 Paris, France

来源：

STATISTICS & PROBABILITY LETTERS | 2007年 / 77卷 / 01期

关键词：

regression with random design; minimax rate of convergence; Besov spaces;

D O I：

10.1016/j.spl.2006.05.010

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：

The problem of estimating a regression function based on a regression model with (known) random design is considered. By adopting the framework of wavelet analysis, we establish the asymptotic minimax rate of convergence under the LP risk over Besov balls. A part of this paper is devoted to the case where the design density is vanishing. (c) 2006 Elsevier B.V. All rights reserved.

引用

页码：40 / 53

页数：14

共 12 条

[1]

Birge L., 2001, NEW LOOK OLD RESULT

[2] Wavelet estimation for samples with random uniform design [J].