On universal oracle inequalities related to high-dimensional linear models

DOI10.1214/10-AOS803zbMath1200.62074arXiv1011.2378MaRDI QIDQ605926

Yuri K. Golubev

Publication date: 15 November 2010

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

Full work available at URL: https://arxiv.org/abs/1011.2378

zbMATH Keywords

oracle inequalityempirical risk minimizationordered smootherexcess riskspectral regularization

Mathematics Subject Classification ID

Multivariate analysis (62H99) Linear regression; mixed models (62J05) Inequalities; stochastic orderings (60E15) Nonparametric estimation (62G05) Bayesian problems; characterization of Bayes procedures (62C10) Eigenvalues, singular values, and eigenvectors (15A18)

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On risk concentration for convex combinations of linear estimators, Solution of linear ill-posed problems using overcomplete dictionaries, Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: A (Numerical) Survey, Ordered smoothers with exponential weighting, Empirical risk minimization as parameter choice rule for general linear regularization methods, Sharp oracle inequalities for aggregation of affine estimators, Adaptive spectral regularizations of high dimensional linear models, Spatially inhomogeneous linear inverse problems with possible singularities, Concentration inequalities for the exponential weighting method, Noisy Laplace deconvolution with error in the operator, Spectral cut-off regularizations for ill-posed linear models, Tikhonov-Phillips regularizations in linear models with blurred design

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