A0150
Title: Robust and consistent variable selection in high-dimensional generalized linear models
Authors: Elvezio Ronchetti - University of Geneva (Switzerland) [presenting]
Marco Avella-Medina - Columbia University (United States)
Abstract: Generalized linear models are popular for modelling a large variety of data. We consider variable selection through penalized methods by focusing on resistance issues in the presence of outlying data and other deviations from assumptions in high dimensions. In particular, we discuss the connections between robustness, sparsity, and oracle properties and the extension of basic robustness concepts to the high-dimensional setting. Specifically, we highlight the weaknesses of widely used penalized M-estimators, propose a robust penalized quasi-likelihood estimator, and show that it enjoys oracle properties in high dimensions and is stable in a neighborhood of the model. We illustrate its finite sample performance on simulated and real data.
