Broken adaptive ridge regression and its asymptotic properties

Linlin Dai, Kani Chen, Zhihua Sun, Zhenqiu Liu, Gang Li

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)334-351
Number of pages18
JournalJournal of Multivariate Analysis
Volume168
DOIs
StatePublished - Nov 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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