Sparse logistic regression: a robust approach

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

Santiago de Compostela

Workshop; Workshop InnPar2D; 2019

Universidad de Santiago de Compostela

Sparse statistical models correspond to situations where there are only a small number of non{zero parameters and for that reason, they are much easier to interpret than dense ones. In this talk, 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 dierent penalizations functions and we introduce the so{called Sign penalization. This new penalty has the advantage that it depends only on one penalty parameter, avoiding arbitrary tuning constants.When a model has a sparse representation, discovering relevant predictive variables is a fundamental goal. We discuss the variable selection ability of the given proposals as well as their asymptotic behaviour. Through a numerical study, we compare the finite sample performance of the proposal corresponding to dierent penalized estimators either robust or classical, under different scenarios. A robust cross{validation criterion is also presented. The analysis of two real data sets enables to investigate the stability of thepenalized estimators to the presence of outliers.