Asymptotic normality of estimating risk upon the wavelet-vaguelette decomposition of a signal function in a model with correlated noise

DOI10.3103/S0278641914030042zbMath1325.62099MaRDI QIDQ2018650

O. V. Shestakov, A. A. Eroshenko

Publication date: 25 March 2015

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

zbMATH Keywords

waveletsasymptotic normalitycorrelated noisethresholdingunbiased risk estimatehomogeneous linear operator

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (2)

Almost everywhere convergence of a wavelet thresholding risk estimate in a model with correlated noise ⋮ Limit distribution of a risk estimate using the vaguelette-wavelet decomposition of signals in a model with correlated noise

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
• Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
• On the asymptotic normality of sequences of weak dependent random variables
• Adapting to Unknown Smoothness via Wavelet Shrinkage
• Ten Lectures on Wavelets
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Ideal spatial adaptation by wavelet shrinkage
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