An extension of Chesneau’s theorem

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• 作者：Junke Kou ; Youming Liu ; ^{liuym@bjut.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：62G07 ; 62G20 ; 42C40
• 刊名：Statistics & Probability Letters
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：108
• 期：Complete
• 页码：23-32
• 全文大小：399 K

文摘

This paper considers a lower bound estimation over $L^p\left({\mathbb{R}}^d\right)(1\le p<\infty )$ risk for d$d$ dimensional regression functions in Besov spaces based on biased data. We provide the best possible lower bound up to a lnn$lnn$ factor by using wavelet methods. When the weight function ω(x,y)≡1$\omega (x,y)\equiv 1$ and 3252b" title="Click to view the MathML source">d=1$d=1$, our result reduces to Chesneau’s theorem, see Chesneau (2007).