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October 2009 High-dimensional variable selection
Larry Wasserman, Kathryn Roeder
Ann. Statist. 37(5A): 2178-2201 (October 2009). DOI: 10.1214/08-AOS646

Abstract

This paper explores the following question: what kind of statistical guarantees can be given when doing variable selection in high-dimensional models? In particular, we look at the error rates and power of some multi-stage regression methods. In the first stage we fit a set of candidate models. In the second stage we select one model by cross-validation. In the third stage we use hypothesis testing to eliminate some variables. We refer to the first two stages as “screening” and the last stage as “cleaning.” We consider three screening methods: the lasso, marginal regression, and forward stepwise regression. Our method gives consistent variable selection under certain conditions.

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Larry Wasserman. Kathryn Roeder. "High-dimensional variable selection." Ann. Statist. 37 (5A) 2178 - 2201, October 2009. https://doi.org/10.1214/08-AOS646

Information

Published: October 2009
First available in Project Euclid: 15 July 2009

zbMATH: 1173.62054
MathSciNet: MR2543689
Digital Object Identifier: 10.1214/08-AOS646

Subjects:
Primary: 62J05
Secondary: 62J07

Keywords: Lasso , Sparsity , stepwise regression

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 5A • October 2009
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