Dynamic tilted current correlation for high dimensional variable screening

Abstract

Variable screening is a commonly used procedure in high dimensional data analysis to reduce dimensionality and ensure the applicability of available statistical methods. Such a procedure is complicated and computationally burdensome because spurious correlations commonly exist among predictor variables, while important predictor variables may not have large marginal correlations with the response variable. To circumvent these issues, in this paper, we develop a new screening technique, the “dynamic tilted current correlation screening” (DTCCS), for high dimensional variable screening. DTCCS is capable of selecting the most relevant predictors within a finite number of steps, and takes the popularly used sure independence screening (SIS) method and the high-dimensional ordinary least squares projection (HOLP) approach as its special cases. The DTCCS technique has sure screening and consistency properties which are justified theoretically and demonstrated numerically. A real example of gene expression data is analyzed using the proposed DTCCS procedure.