Thresholding algorithms, maxisets and well-concentrated bases

By Gerard Kerkyacharian, Dominique Picard, Lucien Birgé, Peter Hall, O. Lepski, Enno Mammen, Alexandre B. Tsybakov. 2000

129 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/ec4a0b8758858266420d49ddd963818e20a75e68

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In Applied Mathematics

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Estimating the intensity of a random measure by histogram type estimators (2006, background): “The results of Kolaczyk and Nowak (2004), which are based on some sort of discretized penalized maximum likelihood estimator in the spirit of Barron and Cover (1991), have some similarity with ours but they assume that the components of the vector s belong to some known interval [c, C], c > 0 and th”
Near optimal thresholding estimation of a Poisson intensity on the real line (2008, methodology): “Let us cite for instance [30], [5] and [7] for respectively thresholding rules, Bayes procedures and kernel estimators.”
Multivariate denoising using wavelets and principal component analysis (2006, methodology): “Such methods are effective because functions f belonging to various general classes are such that they admit a sparse wavelet representation (Kerkyacharian and Picard, 2000).”
Regression in random design and warped wavelets (2004, methodology): “As is proved in [27], generally speaking (but with a mathematical sense that will be detailed later) thresholding methods are working especially well in Lp-risk, not only if one thresholds the wavelet coefficients but also if one thresholds the coefficients associated to a ’well adapted basis’ {ei, ”
Nonlinear estimation for linear inverse problems with error in the operator (2008, background): “2(kˆgε−PJgkHt +kKˆδ−KJk (V J,k•kBs p,p )→HtkfJkBs p,p ). Because of kKˆ−1 δ k (VJ,k•k Ht)→L2 ≤τ, the assertion on Ω II ρ,δ,J follows from the standard risk estimate in Ht-loss (cf. Proposition 7.3 or [14], Theorem 3.1) E[kgˆε−PJgk2 Ht].T (ε)2r(s,t,d), from the operator norm estimate of Proposition 7”
Gaussian model selection (2001, methodology): “…papers starting with Donoho and Johnstone (1994), (see references in Donoho and Johnstone, 1998) and by Kerkyacharian and Picard (see, for instance, Kerkyacharian and Picard, 2000 and the references therein), Lepskii’s method starting with Lepskii (1990, 1991) and adaptive local polynomial fit as…”