Open Access
April 1996 Function estimation via wavelet shrinkage for long-memory data
Yazhen Wang
Ann. Statist. 24(2): 466-484 (April 1996). DOI: 10.1214/aos/1032894449


In this article we study function estimation via wavelet shrinkage for data with long-range dependence. We propose a fractional Gaussian noise model to approximate nonparametric regression with long-range dependence and establish asymptotics for minimax risks. Because of long-range dependence, the minimax risk and the minimax linear risk converge to 0 at rates that differ from those for data with independence or short-range dependence. Wavelet estimates with best selection of resolution level-dependent threshold achieve minimax rates over a wide range of spaces. Cross-validation for dependent data is proposed to select the optimal threshold. The wavelet estimates significantly outperform linear estimates. The key to proving the asymptotic results is a wavelet-vaguelette decomposition which decorrelates fractional Gaussian noise. Such wavelet-vaguelette decomposition is also very useful in fractal signal processing.


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Yazhen Wang. "Function estimation via wavelet shrinkage for long-memory data." Ann. Statist. 24 (2) 466 - 484, April 1996.


Published: April 1996
First available in Project Euclid: 24 September 2002

zbMATH: 0859.62042
MathSciNet: MR1394972
Digital Object Identifier: 10.1214/aos/1032894449

Primary: 42C15 , 62C20 , 62G07

Keywords: cross-validation , fractional Brownian motion , fractional Gaussian noise , fractional Gaussian noise model , long-range dependence , minimax risk , Nonparametric regression , threshold , vaguelette , ‎wavelet , wavelet-vaguelette ecomposition

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 2 • April 1996
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