Stable correlation and robust feature screening
The distance correlation (DC) proposed in \url{doi:10.1214/009053607000000505} is a measure of dependence between random vectors in terms of the characteristic functions and a weight function. In this paper, the authors propose a new correlation, called stable correlation, to measure the dependence between two random vectors by taking a different weight function from the one used in the DC, which is zero if and only if the two random vectors are independent. Different from the DC, this correlation does not require any moment conditions on both random vectors. They further study its other theoretical properties. In terms of the proposed correlation, they present a robust model-free feature screening procedure, named as SC-SIS, for ultrahigh dimensional data and establish its sure screening property and rank consistency property without imposing the sub-exponential or sub-Gaussian tail condition, which is commonly required in the literature of feature screening. In addition, they carry out the finite sample study of the SC-SIS via Monte Carlo simulation and give a real data example, where the performance of the SC-SIS is compared with that of its competitors including the distance correlation sure independence screening procedure. The numerical studies demonstrate that the SC-SIS is able to capture both linear and nonlinear dependence between predictors and responses and is robust against outliers.
scientific article; zbMATH DE number 7462123
scientific article