POINTWISE CONVERGENCE OF THE WAVELET REGULARIZED ESTIMATORS

Abstract

ABSTRACT The classical nonparametric regression problem is considered under the hypothesis of nonnecessarily equispaced deterministic design, white noise, and regression functions belonging to Sobolev spaces. A linear shrinkage wavelet estimator is considered. We prove that this estimator reaches the optimal rate of convergence in the MSE (Mean Squared Error) at any given point. The performance of the estimator is illustrated on a set of standard test functions.