Wavelet threshold estimation of a regression function with random design

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 B-p, q(s) is probed under general assumptions. The adaptive wavelet threshold estimator with near-optimal convergence rate in a Aide range of Besov scale is also constructed. (C) 2001 Elsevier Science.