TY - JOUR
T1 - Broken adaptive ridge regression and its asymptotic properties
AU - Dai, Linlin
AU - Chen, Kani
AU - Sun, Zhihua
AU - Liu, Zhenqiu
AU - Li, Gang
N1 - Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/11
Y1 - 2018/11
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jmva.2018.08.007
DO - 10.1016/j.jmva.2018.08.007
M3 - Article
C2 - 30911202
AN - SCOPUS:85052873091
SN - 0047-259X
VL - 168
SP - 334
EP - 351
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -