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Penalized robust estimators in sparse logistic regression

Author

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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)

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.

Suggested Citation

  • Ana M. Bianco & Graciela Boente & Gonzalo Chebi, 2022. "Penalized robust estimators in sparse logistic regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 563-594, September.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:3:d:10.1007_s11749-021-00792-w
    DOI: 10.1007/s11749-021-00792-w
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    References listed on IDEAS

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    Cited by:

    1. Mingrui Zhong & Zanhua Yin & Zhichao Wang, 2023. "Variable Selection for Sparse Logistic Regression with Grouped Variables," Mathematics, MDPI, vol. 11(24), pages 1-21, December.
    2. Dries Cornilly & Lise Tubex & Stefan Van Aelst & Tim Verdonck, 2024. "Robust and sparse logistic regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(3), pages 663-679, September.

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