Title :
Function estimation via wavelets for data with long-range dependence
Author_Institution :
Dept. of Stat., Missouri Univ., Columbia, MO, USA
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
Keywords :
Gaussian noise; estimation theory; functional analysis; minimax techniques; signal processing; wavelet transforms; asymptotics; fractional Gaussian noise model; function estimation; long-range dependence; minimax risks; noise decorrelation; signal processing; wavelet estimates; wavelet-vaguelette decomposition; Brownian motion; Decorrelation; Gaussian noise; Geophysics; Hydrology; Image generation; Minimax techniques; Noise generators; Signal processing; Statistics;
Conference_Titel :
Information Theory and Statistics, 1994. Proceedings., 1994 IEEE-IMS Workshop on
Conference_Location :
Alexandria, VA
Print_ISBN :
0-7803-2761-6
DOI :
10.1109/WITS.1994.513927