Asymptotic oracle properties of SCAD-penalized least squares estimators

TL;DR

This paper investigates the asymptotic properties of the SCAD-penalized least squares estimator in high-dimensional linear regression, demonstrating its consistency for variable selection and asymptotic normality of nonzero coefficient estimates.

Contribution

It establishes the oracle properties of the SCAD-penalized estimator in high-dimensional settings, extending previous results to cases where the number of covariates grows with sample size.

Findings

Estimator is consistent for variable selection

Nonzero coefficient estimators are asymptotically normal

Simulation shows good performance in variable selection and estimation

Abstract

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.