Function estimation via wavelet shrinkage for long-memory data

• 成果类型: Article
• 署名作者: Wang, YZ
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 466-484
• 关键词: fractional brownian-motion; DENSITY-ESTIMATION; CONVERGENCE; DECOMPOSITION; noise; rates

摘要

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.