  Regression analysis has always been a hot research topic in statistics. We
propose a very flexible semi-parametric regression model called Elliptical
Copula Regression (ECR) model, which covers a large class of linear and
nonlinear regression models such as additive regression model,single index
model. Besides, ECR model can capture the heavy-tail characteristic and tail
dependence between variables, thus it could be widely applied in many areas
such as econometrics and finance. In this paper we mainly focus on the feature
screening problem for ECR model in ultra-high dimensional setting. We propose a
doubly robust sure screening procedure for ECR model, in which two types of
correlation coefficient are involved: Kendall tau correlation and Canonical
correlation. Theoretical analysis shows that the procedure enjoys sure
screening property, i.e., with probability tending to 1, the screening
procedure selects out all important variables and substantially reduces the
dimensionality to a moderate size against the sample size. Thorough numerical
studies are conducted to illustrate its advantage over existing sure
independence screening methods and thus it can be used as a safe replacement of
the existing procedures in practice. At last, the proposed procedure is applied
on a gene-expression real data set to show its empirical usefulness.
