The Annals of Statistics

Wavelet thresholding for nonnecessarily Gaussian noise: Functionality

R. Averkamp and C. Houdré

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 25 November 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1132936560

Digital Object Identifier
doi:10.1214/009053605000000471

Mathematical Reviews number (MathSciNet)
MR2211083

Zentralblatt MATH identifier
1086.62043

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

Keywords
Wavelets thresholding minimax

Citation

Averkamp, R.; Houdré, C. Wavelet thresholding for nonnecessarily Gaussian noise: Functionality. Ann. Statist. 33 (2005), no. 5, 2164--2193. doi:10.1214/009053605000000471. https://projecteuclid.org/euclid.aos/1132936560


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References

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