Wavelet threshold estimation of a regression function with random design

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 Bps, 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. © 2001 Elsevier Science.