Function estimation via wavelet shrinkage for long-memory data

Wang, Yazhen

Ann. Statist., Tome 24 (1996) no. 6, p. 466-484 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1996-04-14
Classification:  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,  62G07,  62C20,  42C15