The Annals of Statistics

Wavelet thresholding for nonnecessarily Gaussian noise: Functionality

R. Averkamp and C. Houdré

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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.

Article information

Ann. Statist., Volume 33, Number 5 (2005), 2164-2193.

First available in Project Euclid: 25 November 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation 62C20: Minimax procedures
Secondary: 60G70: Extreme value theory; extremal processes 41A25: Rate of convergence, degree of approximation

Wavelets thresholding minimax


Averkamp, R.; Houdré, C. Wavelet thresholding for nonnecessarily Gaussian noise: Functionality. Ann. Statist. 33 (2005), no. 5, 2164--2193. doi:10.1214/009053605000000471.

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