Elsevier

Journal of Multivariate Analysis

Volume 168, November 2018, Pages 334-351
Journal of Multivariate Analysis

Broken adaptive ridge regression and its asymptotic properties

https://doi.org/10.1016/j.jmva.2018.08.007Get rights and content
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Abstract

This paper studies the asymptotic properties of a sparse linear regression estimator, referred to as broken adaptive ridge (BAR) estimator, resulting from an L0-based iteratively reweighted L2 penalization algorithm using the ridge estimator as its initial value. We show that the BAR estimator is consistent for variable selection and has an oracle property for parameter estimation. Moreover, we show that the BAR estimator possesses a grouping effect: highly correlated covariates are naturally grouped together, which is a desirable property not known for other oracle variable selection methods. Lastly, we combine BAR with a sparsity-restricted least squares estimator and give conditions under which the resulting two-stage sparse regression method is selection and estimation consistent in addition to having the grouping property in high- or ultrahigh-dimensional settings. Numerical studies are conducted to investigate and illustrate the operating characteristics of the BAR method in comparison with other methods.

AMS subject classification

62J05
62J07

Keywords

Feature selection
Grouping effect
L0-penalized regression
Oracle estimator
Sparsity recovery

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