  This paper is concerned with screening features in ultrahigh dimensional data
analysis, which has become increasingly important in diverse scientific fields.
We develop a sure independence screening procedure based on the distance
correlation (DC-SIS, for short). The DC-SIS can be implemented as easily as the
sure independence screening procedure based on the Pearson correlation (SIS,
for short) proposed by Fan and Lv (2008). However, the DC-SIS can significantly
improve the SIS. Fan and Lv (2008) established the sure screening property for
the SIS based on linear models, but the sure screening property is valid for
the DC-SIS under more general settings including linear models. Furthermore,
the implementation of the DC-SIS does not require model specification (e.g.,
linear model or generalized linear model) for responses or predictors. This is
a very appealing property in ultrahigh dimensional data analysis. Moreover, the
DC-SIS can be used directly to screen grouped predictor variables and for
multivariate response variables. We establish the sure screening property for
the DC-SIS, and conduct simulations to examine its finite sample performance.
Numerical comparison indicates that the DC-SIS performs much better than the
SIS in various models. We also illustrate the DC-SIS through a real data
example.
