Limit distribution of a risk estimate using the vaguelette-wavelet decomposition of signals in a model with correlated noise

DOI10.3103/S0278641915010021zbMath1357.94032MaRDI QIDQ2356506

A. A. Eroshenko, O. V. Shestakov, Andrey A. Kudryavtsev

Publication date: 30 July 2015

Published in: Moscow University Computational Mathematics and Cybernetics (Search for Journal in Brave)

zbMATH Keywords

waveletsasymptotic normalitycorrelated noisethresholdingunbiased risk estimate

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Inference from stochastic processes and spectral analysis (62M15) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Cites Work

• Basic properties of strong mixing conditions. A survey and some open questions
• Consistency of risk estimation with thresholding of wavelet coefficients
• Asymptotic normality of adaptive wavelet thresholding risk estimation
• On the asymptotic normality of sequences of weak dependent random variables
• Asymptotic normality of estimating risk upon the wavelet-vaguelette decomposition of a signal function in a model with correlated noise
• Adapting to Unknown Smoothness via Wavelet Shrinkage
• Wavelet decomposition approaches to statistical inverse problems
• Ten Lectures on Wavelets
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Ideal spatial adaptation by wavelet shrinkage
• Regularization of Wavelet Approximations
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