Function estimation via wavelets for data with long-range dependence

Abstract

Traditionally, processes with long-range dependence have been mathematically awkward to manipulate. This has made the solution of many of the classical signal processing problems involving these processes rather difficult. For a fractional Gaussian noise model, we derive asymptotics for minimax risks and show that wavelet estimates can achieve minimax over a wide range of spaces. This article also establishes a wavelet-vaguelette decomposition (WVD) to decorrelate fractional Gaussian noise.