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VOL. 55 | 2007 Asymptotic oracle properties of SCAD-penalized least squares estimators
Jian Huang, Huiliang Xie

Editor(s) Eric A. Cator, Geurt Jongbloed, Cor Kraaikamp, Hendrik P. Lopuhaä, Jon A. Wellner


We study the asymptotic properties of the SCAD-penalized least squares estimator in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We are particularly interested in the use of this estimator for simultaneous variable selection and estimation. We show that under appropriate conditions, the SCAD-penalized least squares estimator is consistent for variable selection and that the estimators of nonzero coefficients have the same asymptotic distribution as they would have if the zero coefficients were known in advance. Simulation studies indicate that this estimator performs well in terms of variable selection and estimation.


Published: 1 January 2007
First available in Project Euclid: 4 December 2007

zbMATH: 1176.62066

Digital Object Identifier: 10.1214/074921707000000337

Primary: 62J07
Secondary: 62E20

Rights: Copyright © 2007, Institute of Mathematical Statistics


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