Variable selection for high-dimensional generalized linear models with the weighted elastic-net procedure

Abstract

High-dimensional data arise frequently in modern applications such as biology, chemometrics, economics, neuroscience and other scientific fields. The common features of high-dimensional data are that many of predictors may not be significant, and there exists high correlation among predictors. Generalized linear models, as the generalization of linear models, also suffer from the collinearity problem. In this paper, combining the nonconvex penalty and ridge regression, we propose the weighted elastic-net to deal with the variable selection of generalized linear models on high dimension and give the theoretical properties of the proposed method with a diverging number of parameters. The finite sample behavior of the proposed method is illustrated with simulation studies and a real data example.

Keywords:

• collinearity
• generalized linear models
• nonconvex penalty
• oracle ridge estimator
• variable selection

MSC:

• Primary: 62J12
• 62J07
• Secondary: 62E20
• 62F12

Acknowledgements

We would like to thank the Editor and two referees for their constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The authors' research was supported by the National Natural Science Foundation of China [Grant No. 11401340], China Postdoctoral Science Foundation [Grant No. 2014M561892].