Incorporating Information on Neighboring Coe cients into Wavelet Estimation

In standard wavelet methods, the empirical wavelet coe cients are thresholded term by term, on the basis of their individual magnitudes. Information on other coe cients has no in uence on the treatment of particular coe cients. We propose and investigate a wavelet shrinkage method that incorporates information on neighboring coe cients into the decision making. The coe cients are considered in overlapping blocks; the treatment of coe cients in the middle of each block depends on the data in the whole block. Both the asymptotic and numerical performances of two particular versions of the estimator are considered. In numerical comparisons with various methods, both versions of the estimator perform excellently; on the theoretical side, we show that one of the versions achieves the exact optimal rates of convergence over a range of Besov classes.