Minimax convergence rates under the Lp-risk in the functional deconvolution model

Abstract

We derive minimax results in the functional deconvolution model under the Lp-risk, 1 ≤ p < ∞. Lower bounds are given when the unknown response function is assumed to belong to a Besov ball and under appropriate smoothness assumptions on the blurring function, including both regular-smooth and super-smooth convolutions. Furthermore, we investigate the asymptotic minimax properties of an adaptive wavelet estimator over a wide range of Besov balls. The new findings extend recently obtained results under the L2-risk. As an illustration, we discuss particular examples for both continuous and discrete settings. © 2009 Elsevier B.V. All rights reserved.