Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis

Abstract

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(n^κ) with some κ ⩾ 0. We assess the finite sample property of the proposed procedure by Monte 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.

• Consistency in ranking
• Sure screening property
• Ultrahigh dimensional data analysis

Additional information

Notes on contributors

Hengjian Cui

Hengjian Cui is Professor, Department of Statistics, Capital Normal University, China (E-mail: [email protected]).

Runze Li

Runze Li is Distinguished Professor, Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, PA 16802-2111 (E-mail: [email protected]).

Wei Zhong

Wei Zhong is Corresponding Author, Assistant Professor, Wang Yanan Institute for Studies in Economics (WISE), Department of Statistics and Fujian Key Laboratory of Statistical Science, Xiamen University, China (E-mail: [email protected]).