The concordance filter: an adaptive model-free feature screening procedure

A new model-free and data-adaptive feature screening procedure referred to as the concordance filter is developed for ultrahigh-dimensional data. The proposed method is based on the concordance filter which measures concordance between random vectors and can work adaptively with several types of predictors and response variables. We apply the concordance filter to deal with feature screening problems emerging from a wide range of real applications, such as nonparametric regression and survival analysis, among others. It is shown that the concordance filter enjoys the sure screening and rank consistency properties under weak regularity conditions. In particular, the concordance filter can still be powerful in the presence of censoring and heavy tails. We further demonstrate the superior performance of the concordance filter over existing screening methods by numerical examples and medical applications.