We study a marginal empirical likelihood approach in scenarios when the
number of variables grows exponentially with the sample size. The marginal
empirical likelihood ratios as functions of the parameters of interest are
systematically examined, and we find that the marginal empirical likelihood
ratio evaluated at zero can be used to differentiate whether an explanatory
variable is contributing to a response variable or not. Based on this finding,
we propose a unified feature screening procedure for linear models and the
generalized linear models. Different from most existing feature screening
approaches that rely on the magnitudes of some marginal estimators to identify
true signals, the proposed screening approach is capable of further
incorporating the level of uncertainties of such estimators. Such a merit
inherits the self-studentization property of the empirical likelihood approach,
and extends the insights of existing feature screening methods. Moreover, we
show that our screening approach is less restrictive to distributional
assumptions, and can be conveniently adapted to be applied in a broad range of
scenarios such as models specified using general moment conditions. Our
theoretical results and extensive numerical examples by simulations and data
analysis demonstrate the merits of the marginal empirical likelihood approach.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1139 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
