关键词: 超高维数据, 特征筛选, 秩能量距离, 确定筛选性质

Abstract: Feature screening is a common method for dimensionality reduction in ultra-high dimensional data analysis.In this paper,a new feature screening procedure,named RED-SIS,is first proposed based on rank-based energy distance.This procedure does not need to assume model structure and finite moment conditions,and is robust for heavy-tailed covariate. Secondly,the asymptotical properties of the proposed method are studied,the sure screening property and ranking consistency property are proved under some mild regularity conditions.It shows that the proposed RED-SIS can effectively deal with the ultra-high dimensional discriminant analysis with the sample size n and the dimension number p satisfying logp=O(nα).Also,as the sample size increases, the screened set contains all true important feature sets with the probability tending to 1.Last,we present the finite sample performance of the proposed method by numerical analysis,and compare the proposed method with the existing methods for the feature screening in ultra-high dimensional discriminant analysis.Both simulation and real data analysis shows that RED-SIS can be more competitive for feature screening with heavy-tailed distribution.

Key words: Ultra-high Dimensional Data, Feature Screening, Rank-based Energy Distance, Sure Screening Property