On the adaptive wavelet deconvolution of a density for strong mixing sequences

Abstract

This paper studies the estimation of a density in the convolution density model from strong mixing observations. The ordinary smooth case is considered. Adopting the minimax approach under the mean integrated square error over Besov balls, we explore the performances of two wavelet estimators: a linear one based on projections and a non-linear one based on a hard thresholding rule. The feature of the non-linear one is to be adaptive, i.e., it does not require any prior knowledge of the smoothness class of the unknown density in its construction. We prove that it attains a fast rate of convergence which corresponds to the optimal one obtained in the standard i.i.d. case up to a logarithmic term.