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Variable selection and collinearity processing for multivariate data via row-elastic-net regularization

Author

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  • Bingzhen Chen

    (Renmin University of China)

  • Wenjuan Zhai

    (Cangzhou Jiaotong College)

  • Lingchen Kong

    (Beijing Jiaotong University)

Abstract

Multivariate data is collected in many fields, such as chemometrics, econometrics, financial engineering and genetics. In multivariate data, heteroscedasticity and collinearity occur frequently. And selecting material predictors is also a key issue when analyzing multivariate data. To accomplish these tasks, multivariate linear regression model is often constructed. We thus propose row-sparse elastic-net regularized multivariate Huber regression model in this paper. For this new model, we proof its grouping effect property and the property of resisting sample outliers. Based on the KKT condition, an accelerated proximal sub-gradient algorithm is designed to solve the proposed model and its convergency is also established. To demonstrate the accuracy and efficiency, simulation and real data experiments are carried out. The numerical results show that the new model can deal with heteroscedasticity and collinearity well.

Suggested Citation

  • Bingzhen Chen & Wenjuan Zhai & Lingchen Kong, 2022. "Variable selection and collinearity processing for multivariate data via row-elastic-net regularization," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(1), pages 79-96, March.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:1:d:10.1007_s10182-021-00403-x
    DOI: 10.1007/s10182-021-00403-x
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    References listed on IDEAS

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    Cited by:

    1. Wentao Qu & Xianchao Xiu & Huangyue Chen & Lingchen Kong, 2023. "A Survey on High-Dimensional Subspace Clustering," Mathematics, MDPI, vol. 11(2), pages 1-39, January.

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