Model-Free Feature Screening for Ultrahigh
Dimensional Discriminant Analysis
Hengjian Cui, Runze Li, Wei Zhong
Journal of the American Statistical Association Vol. 110, No. 510
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This work is concerned with marginal sure independence feature screening for ultrahigh dimensional discriminant analysis. The response
variable is categorical in discriminant analysis. This enables us to use the conditional distribution function to construct a new index for
feature screening. In this article, we propose a marginal feature screening procedure based on empirical conditional distribution function.
We establish the sure screening and ranking consistency properties for the proposed procedure without assuming any moment condition on
the predictors. The proposed procedure enjoys several appealing merits. First, it is model-free in that its implementation does not require
specification of a regression model. Second, it is robust to heavy-tailed distributions of predictors and the presence of potential outliers.
Third, it allows the categorical response having a diverging number of classes in the order of O(nκ ) with some κ ≥ 0. We assess the finite
sample property of the proposed procedure byMonte Carlo simulation studies and numerical comparison.We further illustrate the proposed
methodology by empirical analyses of two real-life datasets. Supplementary materials for this article are available online.
Keywords: Consistency in ranking; Sure screening property; Ultrahigh dimensional data analysis