Quadratic discriminant analysis (QDA) is a widely used statistical tool to classify observations from different multivariate Normal populations. The generalized quadratic discriminant analysis (GQDA) classification rule/classifier, which generalizes the QDA and the minimum Mahalanobis distance (MMD) classifiers to discriminate between populations with underlying elliptically symmetric distributions competes quite favorably with the QDA classifier when it is optimal and performs much better when QDA fails under non-Normal underlying distributions with heavy tail, e.g. Cauchy distribution. However, the classification rule in GQDA is still based on the sample mean vector and the sample dispersion matrix of a training set, which are extremely non-robust under data contamination. In real world, however, it is quite common to face data which are highly vulnerable to outliers and so the lack of robustness of the classical estimators of the mean vector and the dispersion matrix reduces the efficiency of the GQDA classifier significantly, increasing the misclassification errors. The present paper investigates the performance of the GQDA classifier when the classical estimators of the mean vector and the dispersion matrix used therein are replaced by various robust counterparts. Applications to various real data sets as well as simulation studies reveal far better performance of the proposed robust versions of the GQDA classifier. A comparative study has been made to advocate the appropriate choice of the robust estimators to be used in a specific situation.

二次判别分析（QDA）是一种广泛使用的统计工具，用于对来自不同多元正态总体的观察结果进行分类。广义二次判别分析（GQDA）分类规则/分类器，对QDA和最小马哈拉诺比斯距离（MMD）分类器进行一般化，以区分具有基本椭圆对称分布的总体，从而在最优且性能更好的情况下与QDA分类器竞争当QDA在具有重尾的非正态基础分布（例如柯西分布）下失败时。但是，GQDA中的分类规则仍然基于训练集的样本均值向量和样本分散矩阵，在数据污染下这些样本极不健壮。但是，在现实世界中，面对极易受到异常值影响的数据是很常见的，因此均值向量和色散矩阵的经典估计量缺乏鲁棒性，这大大降低了GQDA分类器的效率，从而增加了误分类错误。本文研究了当均值向量的经典估计量和其中使用的色散矩阵被各种健壮的对等物代替时，GQDA分类器的性能。在各种实际数据集以及仿真研究中的应用表明，GQDA分类器的建议健壮版本的性能要好得多。比较研究已经取得了倡导稳健估计的适当选择在特定的情况下使用。