Function Estimation via Wavelet Shrinkage
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.
منابع مشابه
Fractal Function Estimation via Wavelet Shrinkage
In scientiic studies objects are often very rough. Mathematically these rough objects are modeled by fractal functions, and fractal dimension is usually used to measure their roughness. The present paper investigates fractal function estimation by wavelet shrinkage. It is shown that wavelet shrinkage can estimate fractal functions with their fractal dimensions virtually preserved.
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