Canonical thresholding for nonsparse high-dimensional linear regression

DOI10.1214/21-AOS2116zbMath1486.62207arXiv2007.12313OpenAlexW3044968142MaRDI QIDQ2119237

Igor Silin, Jianqing Fan

Publication date: 23 March 2022

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

Full work available at URL: https://arxiv.org/abs/2007.12313

zbMATH Keywords

thresholdingprincipal component regressionhigh-dimensional linear regressionrelative errorscovariance eigenvalues decay

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05)

Uses Software

• WONDER

Cites Work

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• Sufficient forecasting using factor models
• Factor-Adjusted Regularized Model Selection
• On the prediction performance of the Lasso
• Asymptotics of cross-validated risk estimation in estimator selection and performance assess\-ment
• SLOPE-adaptive variable selection via convex optimization
• ``Preconditioning for feature selection and regression in high-dimensional problems
• Persistene in high-dimensional linear predictor-selection and the virtue of overparametrization
• Minimax estimation via wavelet shrinkage
• A distribution-free theory of nonparametric regression
• Least angle regression. (With discussion)
• On the conditions used to prove oracle results for the Lasso
• Slope meets Lasso: improved oracle bounds and optimality
• Distributed linear regression by averaging
• Just interpolate: kernel ``ridgeless regression can generalize
• Simultaneous analysis of Lasso and Dantzig selector
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• Adapting to Unknown Smoothness via Wavelet Shrinkage
• Test of Significance Based on Wavelet Thresholding and Neyman's Truncation
• Ideal spatial adaptation by wavelet shrinkage
• Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
• De-noising by soft-thresholding
• WONDER: Weighted one-shot distributed ridge regression in high dimensions
• Two Models of Double Descent for Weak Features
• Benign overfitting in linear regression
• Statistical Foundations of Data Science
• Minimax Rates of Estimation for High-Dimensional Linear Regression Over $\ell_q$-Balls
• Prediction by Supervised Principal Components