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Wavelet thresholding for nonnecessarily Gaussian noise: functionality. (English) Zbl 1086.62043

Summary: 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.

MSC:

62G07 Density estimation
62C20 Minimax procedures in statistical decision theory
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
41A25 Rate of convergence, degree of approximation
60G35 Signal detection and filtering (aspects of stochastic processes)
62M99 Inference from stochastic processes
62M20 Inference from stochastic processes and prediction
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