Gini distance correlation (GDC) was recently proposed to measure the dependence between a categorical variable, Y, and a numerical random vector, X. It mutually characterizes independence between X and Y. In this article, we utilize the GDC to establish a feature screening for ultrahigh-dimensional discriminant analysis where the response variable is categorical. It can be used for screening individual features as well as grouped features. The proposed procedure possesses several appealing properties. It is model-free. No model specification is needed. It holds the sure independence screening property and the ranking consistency property. The proposed screening method can also deal with the case that the response has divergent number of categories. We conduct several Monte Carlo simulation studies to examine the finite sample performance of the proposed screening procedure. Real data analysis for two real life datasets are illustrated.

翻译：基尼距离相关（GDC）是近期提出的一种用于衡量分类变量Y与数值随机向量X之间依赖关系的度量，它能相互刻画X与Y的独立性。本文利用GDC为响应变量为分类变量的超高维判别分析建立特征筛选方法。该方法既可筛选单个特征，也可筛选分组特征。所提出的筛选过程具有若干优良性质：它是无模型的，无需指定模型形式；具备确定独立性筛选性质和排序一致性性质；还能处理响应类别数发散的情形。我们通过多项蒙特卡洛模拟研究检验了所提筛选方法在有限样本下的表现，并基于两个真实数据集进行了实际数据分析。