Wavelet thresholding for nonnecessarily Gaussian noise: functionality

Abstract

For signals belonging to balls in smoothness classes and noise with enough moments, the asymptotic behavior of the minimax quadratic risk among soft-threshold estimates is investigated. In turn, these results, combined with a median filtering method, lead to asymptotics for denoising heavy tails via wavelet thresholding. Some further comparisons of wavelet thresholding and of kernel estimators are also briefly discussed.

Published at http://dx.doi.org/10.1214/009053605000000471 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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