Wavelet block thresholding for samples with random design: a minimax approach under the Lp risk

Abstract

We consider the regression model with (known) random design. We investigate the minimax performances of an adaptive wavelet block thresholding estimator under the L^p risk with p≥2 over Besov balls. We prove that it is near optimal and that it achieves better rates of convergence than the conventional term-by-term estimators (hard, soft,…).