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A data-driven block thresholding approach to wavelet estimation. (English) Zbl 1162.62032
Summary: 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 C. M. Stein’s [ibid. 9, 1135–1151 (1981; Zbl 0476.62035)] unbiased risk estimate. The estimator is sharp adaptive over a class of Besov bodies and achieves simultaneously within a small constant factor of the minimax risk over a wide collection of Besov bodies including both the “dense” and “sparse” cases. The procedure is easy to implement. Numerical results show that it has superior finite sample performance in comparison to the other leading wavelet thresholding estimators.

MSC:
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65C60 Computational problems in statistics (MSC2010)
Software:
EBayesThresh
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References:
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