Shengmei He, Shuangge Ma, Wangli Xu

【Abstract】

Cui et al. (2015) proposed a mean–variance feature-screening method based on the index MV(X|Y). By modifying MV(X|Y) with a weight function, a new index AD(X,Y) is introduced to measure the dependence between X and Y, and a corresponding feature-screening procedure called Anderson–Darling sure independence screening (AD-SIS) is proposed for ultrahigh-dimensional discriminant analysis. The sure screening and ranking consistency properties are established under mild conditions. It is shown that AD-SIS is model free with no specification of model structure and can be applied to multi-classification. Furthermore, AD-SIS is robust against heavy-tailed distributions. As such, it can be used to identify the tail difference for the covariate’s distribution. The finite-sample performance of AD-SIS is assessed by simulation and real data analysis. The results show that, compared with existing methods, AD-SIS can be more competitive for feature screening for ultrahigh-dimensional discriminant analysis.

【Keywords】

ultrahigh-dimensional data, feature screening, sure screening, model free