Abstract: Johnstone and Silverman (1997) 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.
Key words and phrases: 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.