Asymptotic Behaviour of Penalized Robust Estimators in Logistic Regression When Dimension Increases

Ana M. Bianco (), Graciela Boente () and Gonzalo Chebi ()
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Ana M. Bianco: Universidad de Buenos Aires and CONICET, Facultad de Ciencias Exactas y Naturales
Graciela Boente: Universidad de Buenos Aires and CONICET, Facultad de Ciencias Exactas y Naturales
Gonzalo Chebi: Universidad de Buenos Aires and CONICET, Facultad de Ciencias Exactas y Naturales

A chapter in Robust and Multivariate Statistical Methods, 2023, pp 323-348 from Springer

Abstract: Abstract In the framework of logistic regression in order to obtain sparse models and automatic variable selection, penalized M-estimators that bound the deviance have been previously studied for fixed dimension. In this chapter, we consider a wide class of M-estimators that involves some well-known robust proposals and study their asymptotic behaviour when the covariates dimension grows to infinity with the sample size. Among other results, we obtain consistency, rates of convergence, and we explore the oracle properties of the regularized M-estimators, for penalty functions of different nature. Specifically, under suitable conditions, we prove that, with probability tending to 1, these estimators only select variables corresponding to non-null true coefficients, and we derive their asymptotic distribution.

Keywords: Logistic regression; High-dimensional covariates; Penalty functions; Robust estimation; Sparsity (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-22687-8_15

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DOI: 10.1007/978-3-031-22687-8_15

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