TY - JOUR
T1 - An extended projection data depth and its applications to discrimination
AU - Cui, Xia
AU - Lin, Lu
AU - Yang, Guangren
N1 - Funding Information:
This article is supported by NNSF project (10771123) of China, NBRP (973 Program 2007CB814901) of China and NSF project (Y2006A13) of Shandong Province of China.
PY - 2008/1
Y1 - 2008/1
N2 - 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.
AB - 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.
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U2 - 10.1080/03610920701858396
DO - 10.1080/03610920701858396
M3 - Article
AN - SCOPUS:46249108557
SN - 0361-0926
VL - 37
SP - 2276
EP - 2290
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 14
ER -