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

Bingzhen Chen (), Wenjuan Zhai () and Lingchen Kong ()
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Bingzhen Chen: Renmin University of China
Wenjuan Zhai: Cangzhou Jiaotong College
Lingchen Kong: Beijing Jiaotong University

AStA Advances in Statistical Analysis, 2022, vol. 106, issue 1, No 4, 79-96

Abstract: 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.

Keywords: Robust estimator; Multivariate linear regression; Collinearity; Row-sparsity; Sub-gradient algorithm; 62H12; 62F12; 62G35; 65K10; 90C46; 90C25 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10182-021-00403-x

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