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April 2008 High-dimensional generalized linear models and the lasso
Sara A. van de Geer
Ann. Statist. 36(2): 614-645 (April 2008). DOI: 10.1214/009053607000000929

Abstract

We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear predictor, after normalization with the empirical norm. The examples include logistic regression, density estimation and classification with hinge loss. Least squares regression is also discussed.

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Sara A. van de Geer. "High-dimensional generalized linear models and the lasso." Ann. Statist. 36 (2) 614 - 645, April 2008. https://doi.org/10.1214/009053607000000929

Information

Published: April 2008
First available in Project Euclid: 13 March 2008

zbMATH: 1138.62323
MathSciNet: MR2396809
Digital Object Identifier: 10.1214/009053607000000929

Subjects:
Primary: 62G08

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 2 • April 2008
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