Function Estimation via Wavelet
نویسنده
چکیده
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 asymp-totics for minimax risks. Because of long-range dependence, the minimax risk and the minimax linear risk converge to zero at rates that diier 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 signiicantly outperform linear estimates. The key to proving the asymptotic results is a wavelet-vaguelette decomposition which decorre-lates fractional Gaussian noise. Such wavelet-vaguelette decomposition is also very useful in fractal signal processing. Runing Head: Wavelet Shrinkage for Long-Memory Data.
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