Robust feature screening for elliptical copula regression model

In this paper, we propose a flexible semi-parametric regression model called Elliptical Copula Regression (ECR) model, which covers a large class of linear and nonlinear regression models such as the additive regression model and the linear transformation model. In addition, ECR model can capture the heavy-tail characteristic and tail dependence between variables, thus it can be widely applied in many areas such as econometrics and finance. We mainly focus on the feature screening problem for ECR model in an ultra-high dimensional setting here. We propose a robust feature screening procedure for ECR model, in which two types of correlation coefficients are involved: Kendall’s τ correlation and canonical correlation. Theoretical analysis shows that the procedure enjoys sure screening property, i.e., with probability tending to 1, the feature 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 feature screening methods. At last, the proposed procedure is applied to a gene-expression real data set to show its empirical usefulness.