We consider the problem of variable screening in
ultra-high-dimensional generalized linear models
(GLMs) of nonpolynomial orders. Since the popular
SIS approach is extremely unstable in the presence
of contamination and noise, we discuss a new robust
screening procedure based on the minimum density
power divergence estimator (MDPDE) of the marginal
regression coefficients. Our proposed screening procedure performs well under pure and contaminated data
scenarios. We provide a theoretical motivation for the
use of marginal MDPDEs for variable screening from
both population as well as sample aspects; in particular, we prove that the marginal MDPDEs are uniformly
consistent leading to the sure screening property of
our proposed algorithm. Finally, we propose an appropriate MDPDE-based extension for robust conditional
screening in GLMs along with the derivation of its sure
screening property. Our proposed methods are illustrated through extensive numerical studies along with
an interesting real data application
