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Broken adaptive ridge regression and its asymptotic properties

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

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.

Suggested Citation

  • Dai, Linlin & Chen, Kani & Sun, Zhihua & Liu, Zhenqiu & Li, Gang, 2018. "Broken adaptive ridge regression and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 334-351.
    • Handle: RePEc:eee:jmvana:v:168:y:2018:i:c:p:334-351
    DOI: 10.1016/j.jmva.2018.08.007
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    Cited by:

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    5. Belli, Edoardo, 2022. "Smoothly adaptively centered ridge estimator," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    6. Zhihua Sun & Yi Liu & Kani Chen & Gang Li, 2022. "Broken adaptive ridge regression for right-censored survival data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 69-91, February.
    7. Takumi Saegusa & Tianzhou Ma & Gang Li & Ying Qing Chen & Mei-Ling Ting Lee, 2020. "Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 376-398, December.
    8. Yuxiang Wu & Hui Zhao & Jianguo Sun, 2023. "Group variable selection for the Cox model with interval‐censored failure time data," Biometrics, The International Biometric Society, vol. 79(4), pages 3082-3095, December.
    9. Dong, Qingkai & Liu, Binxia & Zhao, Hui, 2023. "Weighted least squares model averaging for accelerated failure time models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).

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