An Extended Projection Data Depth and Its Applications to Discrimination

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.