Adaptive spectral regularizations of high dimensional linear models

DOI10.1214/11-EJS649zbMath1271.62146arXiv1112.5890MaRDI QIDQ1952239

Yuri K. Golubev

Publication date: 28 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.5890

zbMATH Keywords

oracle inequalityempirical risk minimizationordered smootherexcess risk

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05)

Related Items

Empirical risk minimization as parameter choice rule for general linear regularization methods, Optimal Adaptation for Early Stopping in Statistical Inverse Problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Risk hull method and regularization by projections of ill-posed inverse problems
• A statistical perspective on ill-posed inverse problems (with discussion)
• On universal oracle inequalities related to high-dimensional linear models
• The principle of penalized empirical risk in severely ill-posed problems
• Local solutions to inverse problems in geodesy. The impact of the noise covariance structure upon the accuracy of estimation
• Optimal filtering of square-integrable signals in Gaussian noise
• Ordered linear smoothers
• Oracle inequalities for inverse problems
• Weak convergence and empirical processes. With applications to statistics
• Adaptive complexity regularization for linear inverse problems
• Minimal penalties for Gaussian model selection
• Fundamentals of Computerized Tomography
• A Lepskij-type stopping rule for regularized Newton methods
• Statistical Inverse Estimation in Hilbert Scales
• Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications
• The Lepskii principle revisited
• An Iteration Formula for Fredholm Integral Equations of the First Kind