Asymptotic behaviour of penalized robust estimators in logistic regression when dimension increases

BIANCO, ANA MARIA; BOENTE BOENTE, GRACIELA LINA; CHEBI GONZALO

Robust and Multivariate Statistical Methods: Festschrift in Honour of David E. Tyler

Springer

Año: 2023;

In the framework of logistic regression in order to obtain sparse models and automaticvariable selection, penalized M􀀀estimators that bound the deviance have been previously studiedfor xed dimension. In this paper, we consider a wide class of M􀀀estimators that involves some wellknown robust proposals and study their asymptotic behaviour when the covariates dimension growsto innity with the sample size. Among other results, we obtain consistency, rates of convergenceand we explore the oracle properties of the regularized M􀀀estimators, for penalty functions ofdierent nature. Specically, under suitable conditions, we prove that, with probability tending to1, these estimators only select variables corresponding to non{null true coecients and we derivetheir asymptotic distribution.