Johnstone, Iain M. Wavelet shrinkage for correlated data and inverse problems: adaptivity results. (English) Zbl 1065.62519 Stat. Sin. 9, No. 1, 51-83 (1999). 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. Cited in 44 Documents MSC: 62G20 Asymptotic properties of nonparametric inference 62G07 Density estimation 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems Keywords:Adaptation; correlated data; fractional Brownian motion; linear inverse problems; long range dependence; mixing conditions; oracle inequalities; rates of convergence; unbiased risk estimate; wavelet vaguelette decomposition; wavelet shrinkage; wavelet thresholding Citations:Zbl 0886.62044 PDFBibTeX XMLCite \textit{I. M. Johnstone}, Stat. Sin. 9, No. 1, 51--83 (1999; Zbl 1065.62519)