Wavelet estimations for density derivatives
Wavelet estimations for density derivatives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.