Asymptotic oracle properties of SCAD-penalized least squares estimators

Details Asymptotic oracle properties of SCAD-penalized least squares estimators Asymptotic oracle properties of SCAD-penalized least squares estimators

2007-09-06

arxiv.org/abs/0709.0863v1

IMS Lecture Notes Monograph Series 2007, Vol. 55, 149-166

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921707000000337 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921707000000337

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.

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