An extended projection data depth and its applications to discrimination

作者：Cui Xia^*; Lin Lu; Yang Guangren

来源：Communications in Statistics - Theory and Methods, 2008, 37(14): 2276-2290.

DOI：10.1080/03610920701858396

• Bayes risk
• breakdown points
• discriminant analysis
• misclassification rate
• projection data depth

This article investigates the possible use of our newly defined extended projection depth (abbreviated to EPD) in nonparametric discriminant analysis. We propose a robust nonparametric classifier, which relies on the intuitively simple notion of EPD. The EPD-based classifier assigns an observation to the population with respect to which it has the maximum EPD. Asymptotic properties of misclassification rates and robust properties of EPD-based classifier are discussed. A few simulated data sets are used to compare the performance of EPD-based classifier with Fisher's linear discriminant rule, quadratic discriminant rule, and PD-based classifier. It is also found that when the underlying distributions are elliptically symmetric, EPD-based classifier is asymptotically equivalent to the optimal Bayes classifier.

• 出版日期2008
• 单位暨南大学; 山东大学