An extension of Chesneau's theorem

被引：11

作者：

Kou, Junke ^{[1
]}

Liu, Youming ^{[1
]}

机构：

[1] Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2016年 / 108卷

基金：

中国国家自然科学基金;

关键词：

Lower bound; Biased regression estimation; L-P risk; Wavelets; REGRESSION;

D O I：

10.1016/j.spl.2015.09.018

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：

This paper considers a lower bound estimation over L-P (R-d) (1 <= p < infinity) risk for d dimensional regression functions in Besov spaces based on biased data. We provide the best possible lower bound up to a Inn factor by using wavelet methods. When the weight function w(x, y) equivalent to 1 and d = 1, our result reduces to Chesneau's theorem, see Chesneau (2007). (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：23 / 32

页数：10

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