On the minimax optimality of block thresholded wavelet estimators with long memory data

Abstract

We consider the estimation of non-parametric regression function with long memory data and investigate the asymptotic rates of convergence of wavelet estimators based on block thresholding. We show that the estimators achieve optimal minimax convergence rates over a large class of functions that involve many irregularities of a wide variety of types, including chirp and Doppler functions, and jump discontinuities. Therefore, in the presence of long memory noise, wavelet estimators still provide extensive adaptivity to many irregularities of large function classes.