Adaptive wavelet estimation of a function in an indirect regression model

Abstract

We consider a nonparametric regression model where m noise-perturbed functions f1,…,fm are randomly observed. For a fixed ν∈{1,…,m}, we want to estimate fν from the observations. To reach this goal, we develop an adaptive wavelet estimator based on a hard thresholding rule. Adopting the mean integrated squared error over Besov balls, we prove that it attains a sharp rate of convergence. Simulation results are reported to support our theoretical findings.