Wavelet estimations for density derivatives

作     者：LIU YouMing WANG HuiYing 

作者机构：Department of Applied Mathematics Beijing University of Technology School of Applied Mathematics Central University of Finance and Economics 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第3期

页      面：483-495页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.11271038) Natural Science Foundation of Beijing (Grant No. 1082003) 

主　　题：wavelet estimators optimality Besov spaces Sobolev spaces density derivative 

摘      要：Donoho et al. in 1996 have made almost perfect achievements in wavelet estimation for a density function f in Besov spaces Bsr,q(R). Motivated by their work, we define new linear and nonlinear wavelet estimators flin,nm, fnonn,m for density derivatives f(m). It turns out that the linear estimation E(‖flinn,m-f(m)‖p) for f(m) ∈ Bsr,q(R) attains the optimal when r≥ p, and the nonlinear one E(‖fnonn,m-f(m)‖p) does the same if r≤p/2(s+m)+1 . In addition, our method is applied to Sobolev spaces with non-negative integer exponents as well.