Function estimation via wavelet shrinkage for long-memory data
Yazhen Wang
Source: Ann. Statist. Volume 24, Number 2
(1996), 466-484.
Abstract
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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Keywords: Long-range dependence; fractional Brownian motion; fractional Gaussian noise; fractional Gaussian noise model; nonparametric regression; minimax risk; vaguelette; wavelet; wavelet-vaguelette ecomposition; threshold; cross-validation
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1032894449
Mathematical Reviews number (MathSciNet): MR1394972
Digital Object Identifier: doi:10.1214/aos/1032894449
Zentralblatt MATH identifier: 0859.62042
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