Robust variable selection via penalized MT-estimator in generalized linear models

Abstract

In this article, we propose penalized MT-estimator to handle simultaneously the problem of parameter estimation and variable selection in generalized linear models. The penalized MT-estimator is based on Valdora and Yohai’s robust MT-estimator and it is shown that for an appropriate penalty function, penalized MT-estimator satisfies oracle property. Penalized MT-estimator efficiently identifies the true model and non-zero coefficients if the sparsity of the true model was known in advance, with probability approaching to one. Main advantage of Penalized MT-estimator is that it produces estimates of non-zero parameters efficiently than the penalized maximum likelihood estimator when the outliers are present in the data. Finally, to examine the performance of the proposed method, simulation studies and a real data example are carried out.

Keywords:

• MT-estimator
• Poisson regression
• SCAD
• variable selection

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62J12

Acknowledgements

The second author would like to acknowledge the financial support from DST-FIST scheme under Grant No. SR/FST/MSI-103 dated 18/11/2015 and UGC-SAP Scheme under Grant No. F.520/8/DRS-I/2016 (SAP-I) dated 8 March 2016.

Additional information

Funding

This work was supported by Department of Science and Technology, Ministry of Science and Technology, New Delhi, India; University Grants Commission, New Delhi, India.