Adaptive wavelet estimation: a block thresholding and oracle inequality approach
نویسندگان
چکیده
منابع مشابه
Adaptive Wavelet Estimation: A Block Thresholding And Oracle Inequality Approach
We study wavelet function estimation via the approach of block thresholding and ideal adaptation with oracle. Oracle inequalities are derived and serve as guides for the selection of smoothing parameters. Based on an oracle inequality and motivated by the data compression and localization properties of wavelets, an adaptive wavelet estimator for nonparametric regression is proposed and the opti...
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A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by minimizing Stein’s unbiased risk estimate. The estimator is sharp adaptive over a class of Besov bodies and achieves simultaneously within a small constant fac...
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Wavelet shrinkage methods have been very successful in nonparametric regression. The most commonly used wavelet procedures achieve adaptivity through term-by-term thresholding. The resulting estimators attain the minimax rates of convergence up to a logarithmic factor. In the present paper, we propose a block thresholding method where wavelet coef-cients are thresholded in blocks, rather than i...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1999
ISSN: 0090-5364
DOI: 10.1214/aos/1018031262