Function Estimation via Wavelet Shrinkage for Long-Memory Data (1996)
| Venue: | Annals of Statistics |
| Citations: | 27 - 5 self |
BibTeX
@ARTICLE{Wang96functionestimation,
author = {Yazhen Wang},
title = {Function Estimation via Wavelet Shrinkage for Long-Memory Data},
journal = {Annals of Statistics},
year = {1996},
volume = {24},
pages = {466--484}
}
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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 zero 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. Runing Head: Wavelet Shrinkage for Long-Memory Data. Key Words: Long...
