Adaptive Wavelet Estimator for a Function and its Derivatives in an Indirect Convolution Model

Abstract

Abstract We consider an indirect convolution model where m blurred and noise-perturbed functions f 1,…,fm are randomly observed. For a fixed ω ε {1,…,m}, we want to estimate f ω and its derivatives. An adaptive nonlinear wavelet estimator using a singular value decomposition is developed. Taking the mean integrated squared error over Besov balls, we prove that it attains a fast rate of convergence.