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

Abstract: Feature screening is useful and popular to detect informative predictors for ultrahigh-dimensional data before developing proceeding statistical analysis or constructing statistical models. While a large body of feature screening procedures has been developed, most of them are restricted on examining 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 proposed by Chatterjee (2020) to develop feature screening procedure. We show that this new screening criterion is able to deal with continuous and discrete responses. Theoretically, sure screening property is established to justify the proposed method. Simulation studies demonstrate that the predictors with nonlinear and oscillatory trajectory are successfully detected regardless of the distribution of the response.