Robust variable selection for generalized linear models with a diverging number of parameters

Abstract

ABSTRACTIn this article, we focus on the problem of robust variable selection for high-dimensional generalized linear models. The proposed procedure is based on smooth-threshold estimating equations and a bounded exponential score function with a tuning parameter γ. The outstanding merit of this new procedure is that it is robust and efficient by selecting automatically the tuning parameter γ based on the observed data, and its performance is superior to some recently developed methods, in particular, when many outliers are included. Furthermore, under some regularity conditions, we have shown that the resulting estimator is -consistent and enjoys the oracle property, when the dimension pn of the predictors satisfies the condition p2n/n → 0, where n is the sample size. Finally, Monte Carlo simulation studies and a real data example are carried out to examine the finite-sample performance of the proposed method.