Stable correlation and robust feature screening

In this paper, we propose a new correlation, called stable correlation, to measure the dependence between two random vectors. The new correlation is well defined without the moment condition and is zero if and only if the two random vectors are independent. We also study its other theoretical properties. Based on the new correlation, we further propose a robust model-free feature screening procedure for ultrahigh dimensional data and establish its sure screening property and rank consistency property without imposing the subexponential or sub-Gaussian tail condition, which is commonly required in the literature of feature screening. We also examine the finite sample performance of the proposed robust feature screening procedure via Monte Carlo simulation studies and illustrate the proposed procedure by a real data example.