Penalized M-estimators for Logistic Regression

BIANCO, ANA; BOENTE, GRACIELA; CHEBI, GONZALO

Viena

Workshop; Data Science, Statistics and Visualization (DSSV 2018); 2018

International Association for Statistical Computing, International Federation for Information Processing, Bernoulli Society, Vienna Data Science Group

We introduce a family of penalized M-type estimators for the logistic regression parameter that are stable against atypical data. We explore different penalizations functions and we introduce the so-called sign penalization. Thisnew penalty has the advantage that it does not shrink the estimated coefficients to 0 and that it depends on only one parameter.Theoretical results regarding oracle properties as well as consistency and asymptotic distribution results are studied. Through a numerical study, we compare the finite sample performance of the proposal with different penalized estimators either robust and classical in different scenarios including clean and contaminated samples.