An extended projection data depth and its applications to discrimination

Xia Cui, Lu Lin, Guangren Yang

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2276-2290
Number of pages15
JournalCommunications in Statistics - Theory and Methods
Volume37
Issue number14
DOIs
StatePublished - Jan 1 2008

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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