``Preconditioning for feature selection and regression in high-dimensional problems

DOI10.1214/009053607000000578zbMath1142.62022arXivmath/0703858OpenAlexW1997840761WikidataQ60691592 ScholiaQ60691592MaRDI QIDQ939656

Debashis Paul, Eric Bair, Robert Tibshirani, Trevor Hastie

Publication date: 28 August 2008

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

Full work available at URL: https://arxiv.org/abs/math/0703858

zbMATH Keywords

prediction errormodel selectionlasso

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Factor analysis and principal components; correspondence analysis (62H25) Ridge regression; shrinkage estimators (Lasso) (62J07) Asymptotic properties of nonparametric inference (62G20)

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Cites Work

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• The Adaptive Lasso and Its Oracle Properties
• Asymptotics for Lasso-type estimators.
• Nonconcave penalized likelihood with a diverging number of parameters.
• Least angle regression. (With discussion)
• High-dimensional graphs and variable selection with the Lasso
• Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
• Adaptive Model Selection
• Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ ¹ minimization
• Prediction by Supervised Principal Components