  Gini distance correlation (GDC) was recently proposed to measure the
dependence between a categorical variable, Y, and a numerical random vector, X.
It mutually characterizes independence between X and Y. In this article, we
utilize the GDC to establish a feature screening for ultrahigh-dimensional
discriminant analysis where the response variable is categorical. It can be
used for screening individual features as well as grouped features. The
proposed procedure possesses several appealing properties. It is model-free. No
model specification is needed. It holds the sure independence screening
property and the ranking consistency property. The proposed screening method
can also deal with the case that the response has divergent number of
categories. We conduct several Monte Carlo simulation studies to examine the
finite sample performance of the proposed screening procedure. Real data
analysis for two real life datasets are illustrated.
