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.
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页码：23 / 32
页数：10
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