Stable correlation and robust feature screening

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