A note of feature screening via a rank-based coefficient of correlation

Feature screening is a useful and popular tool to detect informative predictors for ultrahigh-dimensional data before developing statistical analysis or constructing statistical models. While a large body of feature screening procedures has been developed, most methods are restricted to examine either continuous or discrete responses. Moreover, even though many model-free feature screening methods have been proposed, additional assumptions are imposed in those methods to ensure their theoretical results. To address those difficulties and provide simple implementation, in this paper we extend the rank-based coefficient of correlation to develop a feature screening procedure. We show that this new screening criterion is able to deal with continuous and binary responses. Theoretically, the sure screening property is established to justify the proposed method. Simulation studies demonstrate that the predictors with nonlinear and oscillatory trajectories are successfully retained regardless of the distribution of the response. Finally, the proposed method is implemented to analyze two microarray datasets.