Michigan Technological University, f1;Heilongjiang University, Harbin, China, f2;Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China, f3;Peking University, Beijing, China, f4
Abstract:
The wavelet threshold estimator of a regression function for the random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov Space Bsp, q is proved under general assumptions. The adaptive wavelet threshold estimator with near-optimal convergence rate in a wide range of Besov scale is also constructed.