Abstract:  This paper is concerned with ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure via the measure of conditional mean dependence based on Copula (CC-SIS, for short). The CC-SIS can be implemented as easily as the sure independence screening procedures which respectively based on the Pearson correlation, conditional mean and distance correlation (SIS, SIRS and DC-SIS, for short) and can significantly improve the performance of feature screening. We establish the sure screening property for the CC-SIS, and conduct simulations to examine its finite sample performance. Numerical comparison indicates that the CC-SIS performs better than the other two methods in various models. At last, we also illustrate the CC-SIS through a real data example.

Key words: Ultrahigh dimensionality, Conditional mean dependence, Copula learning; Semiparametric method