Gini Correlation for Feature Screening

In this paper we propose the Gini correlation screening(GCS) method to select the important variables with ultrahigh dimensional data. The new procedure is based on the Gini correlation coefficient via the covariance between the response and the rank of the predictor variables rather than the Pearson correlation and the Kendall τ correlation coefficient. The new method does not require imposing a specific model structure on regression functions and only needs the condition which the predictors and response have continuous distribution function. We demonstrate that, with the number of predictors growing at an exponential rate of the sample size, the proposed procedure possesses consistency in ranking, which is both useful in its own right and can lead to consistency in selection. The procedure is computationally efficient and simple, and exhibits a competent empirical performance in our intensive simulations and real data analysis.