Penalized robust estimators in sparse logistic regression

Ana M. Bianco (), Graciela Boente () and Gonzalo Chebi ()
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Ana M. Bianco: Universidad de Buenos Aires and CONICET
Graciela Boente: Universidad de Buenos Aires and CONICET
Gonzalo Chebi: Universidad de Buenos Aires and CONICET

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2022, vol. 31, issue 3, No 1, 563-594

Abstract: Abstract Sparse covariates are frequent in classification and regression problems where the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are only a small number of nonzero parameters, and for that reason, they are much easier to interpret than dense ones. In this paper, we focus on the logistic regression model and our aim is to address robust and penalized estimation for the regression parameter. We introduce a family of penalized weighted M-type estimators for the logistic regression parameter that are stable against atypical data. We explore different penalization functions including the so-called Sign penalty. We provide a careful analysis of the estimators convergence rates as well as their variable selection capability and asymptotic distribution for fixed and random penalties. A robust cross-validation criterion is also proposed. Through a numerical study, we compare the finite sample performance of the classical and robust penalized estimators, under different contamination scenarios. The analysis of real datasets enables to investigate the stability of the penalized estimators in the presence of outliers.

Keywords: Logistic regression; Outliers; Penalty functions; Robust estimation; Sparse models; 62F35; 62F12 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11749-021-00792-w

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