Robust composite weighted quantile screening for ultrahigh dimensional discriminant analysis

This paper is concerned with feature screening for the ultrahigh dimensional discriminant analysis. A new feature screening procedure based on the conditional quantile is proposed. The proposed procedure has some desirable features. First, it is model-free which does not require specific discriminant model and can be directly applied to the multi-categories situation. Second, it is robust against heavy-tailed distributions, potential outliers and the sample shortage for some categories, which are very common for high dimensional data. We establish the sure screening property and ranking consistency property of the proposed procedure under some regular conditions. Simulation studies and a real data example are used to assess its finite sample performance.