Robust variable selection via penalized MT-estimator in generalized linear models. Issue 22 (21st September 2021)

• Record Type: Journal Article
• Authors: Salamwade, R. L.; Sakate, D. M.
• Is Part Of: Communications in statistics. Volume 51:Issue 22(2022)
• Page Start: 8053
• Page End: 8065
• Publication Date: 2021-09-21
• Subjects: MT-estimator -- Poisson regression -- SCAD -- variable selection; 62J12; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2021.1887240
• Languages: English
• ISSNs: 0361-0926

Abstract

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.