Wavelet Estimation of Function Derivatives from a Multichannel Deconvolution Model

Abstract

This paper considers a multichannel deconvolution model with Gaussian white noises. The goal is to estimate the $d$ -th derivatives of an unknown function in the model. For super-smooth case, we construct an adaptive linear wavelet estimator by wavelet projection method. For regular-smooth case, we provide an adaptive nonlinear wavelet estimator by hard-thresholded method. In order to measure the global performances of our estimators, we show upper bounds on convergence rates using the $L^p$ -risk ( $1\le p<\infty$ ).