Sharp adaptation for inverse problems with random noise

By Laurent Cavalier, Alexandre B. Tsybakov. 2002

191 citations recorded by the source corpus.

Subfields: Mathematical Physics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7b0d98a2e1c773dc0dade2accb4e375b2c0d287c

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Citations in the corpus

Periodic boxcar deconvolution and diophantine approximation (2004, background): “This methodology is now quite well established on other inverse problems with monotone eigenvalues; see, for example, Cavalier and Tsybakov (2002).”
Sharp Oracle Inequalities for Aggregation of Affine Estimators (2011, methodology): “If Σ is diagonal, then for any λ ∈ Λ and for any β ≥ 8 Σ , In the case Σ = I n × n , this result is comparable to [43, p. 20, Thm. 2.49], which states that in the homoscedastic regression model (Σ = I n × n ), EWA acting on two-block positive-part James-Stein estimators satisﬁes, for any λ ∈ Λ such ”
Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations (2000, background): “…much attention has been concentrated on developing adaptive nonparametric estimators both for direct and indirect observations (Lepskii(1991), Donoho and Johnstone (1994), Barron, Birge, Massart (1999), Donoho (1995), Abramovich and Silverman (1998), Johnstone (1999), Cavalier and Tsybakov (1998)).”
Sharp Adaptive Estimation of Linear Functionals (2001, background): “…exist several results on exact asymptotics in minimax adaptation: Efroimovich and Pinsker (1984), Gobubev and Nussbaum (1990), Nemirovski (2000), Cavalier and Tsybakov (2000) (estimation of f in the L2-norm), Lepski (1992b), Tsybakov (1998) (estimation in sup-norm), Lepski and Spokoiny (1997),…”
Oracle inequalities for inverse problems (2002, methodology): “Other oracle inequalities for inverse problems have been proposed recently by Johnstone (1999) and Cavalier and Tsybakov (2002). Johnstone (1999) deals with a class of nonlinear estimators based on soft thresholding in a wavelet context.”
Risk hull method and regularization by projections of ill-posed inverse problems (2006, unknown): “The Annals of Statistics 2006, Vol. 34, No. 4, 1653–1677 DOI: 10.1214/009053606000000542 © Institute of Mathematical Statistics, 2006”
Bayes procedures for adaptive inference in inverse problems for the white noise model (2012, methodology): “For nonparametric inverse problems, the construction of an adaptive estimator based on a properly penalized blockwise Stein’s rule has been studied in [12], cf.”
ON BLOCK THRESHOLDING IN WAVELET REGRESSION: ADAPTIVITY, BLOCK SIZE, AND THRESHOLD LEVEL (2002, methodology): “Besides nonparametric regression, block thresholding techniques can be applied to other statistical problems such as linear inverse problems (see Cai (2000a) and Cavalier and Tsybakov (2000)).”
Adaptive Global Testing for Functional Linear Models (2014, methodology): “Similar conditions are considered in estimating θ , such as Cavalier and Tsybakov (2002) for the white-noise and Gaussian sequence models, and Hall and Horowitz (2007), Meister (2011) for functional linear regression.”
Thresholding estimators for linear inverse problems and deconvolutions (2003, background): “This power law deconvolution has been studied by many authors [26, 8].”