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