Wavelet thresholding for non-necessarily Gaussian noise: idealism

DOI10.1214/aos/1046294459zbMath1102.62329OpenAlexW2051539380MaRDI QIDQ1394759

Christian Houdré, Roland Averkamp

Publication date: 2003

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1046294459

zbMATH Keywords

waveletsminimaxthresholding

Mathematics Subject Classification ID

Density estimation (62G07) Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40)

Related Items (16)

Sharp Khinchin-type inequalities for symmetric discrete uniform random variables ⋮ Wavelet thresholding for nonnecessarily Gaussian noise: functionality ⋮ Robust wavelet estimation to eliminate simultaneously the effects of boundary problems, outliers, and correlated noise ⋮ De-noising option prices with the wavelet method ⋮ Sharp Rosenthal‐type inequalities for mixtures and log‐concave variables ⋮ Wavelet shrinkage in nonparametric regression models with positive noise ⋮ Multiscale Methods for Data on Graphs and Irregular Multidimensional Situations ⋮ Hybrid generalized empirical likelihood estimators: instrument selection with adaptive lasso ⋮ From Ball's cube slicing inequality to Khinchin-type inequalities for negative moments ⋮ Wavelet-based option pricing: an empirical study ⋮ Robust nonparametric estimation via wavelet median regression ⋮ Stein estimation for infinitely divisible laws ⋮ A wavelet-based hybrid approach to estimate variance function in heteroscedastic regression models ⋮ Gaussian mixtures: entropy and geometric inequalities ⋮ Penalized wavelet estimation and robust denoising for irregular spaced data ⋮ On the posterior median estimators of possibly sparse sequences

Uses Software

• S+WAVELETS

Cites Work

• Mathematical theory of statistics. Statistical experiments and asymptotic decision theory
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• Density estimation by kernel and wavelets methods: optimality of Besov spaces
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• Neo-classical minimax problems, thresholding and adaptive function estimation
• Extrema of the Distributions of Quadratic Forms of Gaussian Variables
• Adapting to Unknown Smoothness via Wavelet Shrinkage
• Ten Lectures on Wavelets
• Ideal spatial adaptation by wavelet shrinkage
• Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage
• De-noising by soft-thresholding
• Limiting the Risk of Bayes and Empirical Bayes Estimators--Part I: The Bayes Case
• Inequalities: theory of majorization and its applications
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