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Wavelet shrinkage for correlated data and inverse problems: adaptivity results. (English) Zbl 1065.62519
Summary: The author and B. W. Silverman [J. R. Stat. Soc., Ser. B 59, No. 2, 319–351 (1997; Zbl 0886.62044)] described a level-dependent thresholding method for extracting signals from correlated noise. The thresholds were chosen to minimize a data based unbiased risk criterion. Here we show that in certain asymptotic models encompassing short and long range dependence, these methods are simultaneously asymptotically minimax up to constants over a broad range of Besov classes. We indicate the extension of the methods and results to a class of linear inverse problems possessing a wavelet vaguelette decomposition.

62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems