The principle of penalized empirical risk in severely ill-posed problems

DOI10.1007/s00440-004-0362-yzbMath1064.62011OpenAlexW2067463233MaRDI QIDQ706328

Yuri K. Golubev

Publication date: 8 February 2005

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-004-0362-y

zbMATH Keywords

penalizationsingular value decompositionpartial differential equationprojection estimatorminimax riskempirical risk

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Minimax procedures in statistical decision theory (62C20)

Related Items (11)

Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: A (Numerical) Survey ⋮ On universal oracle inequalities related to high-dimensional linear models ⋮ Empirical risk minimization as parameter choice rule for general linear regularization methods ⋮ Adaptive spectral regularizations of high dimensional linear models ⋮ Multichannel deconvolution with long-range dependence: a minimax study ⋮ Risk hull method and regularization by projections of ill-posed inverse problems ⋮ Quadratic functional estimation in inverse problems ⋮ On convergence rates equivalency and sampling strategies in functional deconvolution models ⋮ Functional deconvolution in a periodic setting: uniform case ⋮ On the stability of the risk hull method for projection estimators ⋮ Risk hull method for spectral regularization in linear statistical inverse problems

Cites Work

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• Optimal filtering of square-integrable signals in Gaussian noise
• Estimation of the mean of a multivariate normal distribution
• Risk bounds for model selection via penalization
• Ordered linear smoothers
• A statistical approach to some inverse problems for partial differential equations
• Oracle inequalities for inverse problems
• Sharp adaptation for inverse problems with random noise
• On minimax filtering over ellipsoids
• On optimal solutions of the deconvolution problem
• An optimal selection of regression variables
• Robust and efficient recovery of a signal passed through a filter and then contaminated by non-Gaussian noise
• On the best rate of adaptive estimation in some inverse problems
• Statistical Inverse Estimation in Hilbert Scales
• Block Thresholding and Sharp Adaptive Estimation in Severely Ill-Posed Inverse Problems
• Some Asymptotic Expansions for Prolate Spheroidal Wave Functions
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty-III: The Dimension of the Space of Essentially Time- and Band-Limited Signals
• Some Comments on C P

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