Title: Screening for ultrahigh-dimensional regression with cellwise outliers
Authors: Stefan Van Aelst - University of Leuven (Belgium) [presenting]
Yixin Wang - University of Leuven (Belgium)
Abstract: In ultrahigh-dimensional data it can easily happen that most or all of the observations are contaminated in some of their cells. To robustly estimate a best approximating subspace in this setting, we consider componentwise LTS-estimators. We propose an efficient algorithm to calculate these estimators by using estimating equations and deterministic starting values. We apply these methods in a robust variable selection procedure for ultra-high dimensional regression analysis. In particular, we propose a robust version of Factor Profiled Sure Independence Screening. By assuming that the predictors can be represented by a few latent factors, this method can handle correlation among the candidate predictors. We use robust componentwise LTS-estimators to estimate the factors. Then, a robust regression method is applied on the profiled variables to screen for the most important predictors.