An extended projection data depth and its applications to discrimination

Communications in Statistics - Theory and Methods

Volumn 37, Issue 14, 2008, Pages 2276-2290

  Cui, Xia ^a   Lin, Lu ^a   Yang, Guangren ^b  

^a SHANDONG UNIVERSITY   (China)

^b JINAN UNIVERSITY   (China)

Author keywords

Bayes risk; Breakdown points; Discriminant analysis; Misclassi fication rate; Projection data depth

Indexed keywords

ASYMPTOTIC ANALYSIS; CLASSIFIERS; DISCRIMINANT ANALYSIS; LEARNING SYSTEMS; POPULATION STATISTICS;

(PL) PROPERTIES; (R ,S)-SYMMETRIC; ASYMPTOTIC PROPERTIES; BAYES CLASSIFIERS; FISHER'S LINEAR DISCRIMINANT (FLD); MISCLASSIFICATION RATES; NON-PARAMETRIC; NONPARAMETRIC DISCRIMINANT ANALYSIS (NDA); PROJECTION DATA; SIMULATED DATA SETS;

CLASSIFICATION (OF INFORMATION);

EID: 46249108557     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920701858396     Document Type: Article

References (17)

1. Christmann, A., Rousseeuw, P. J. (2001). Measuring overlap in logistic regression. Comput. Statist. Data. Anal. 37:65-75.
2. Christmann, A., Fischer, P., Joachims, T. (2002). Comparison between various regression depth methods and the support vector machine to approximate the minimum number of misclassifications. Comput. Statist. 17:273-287.
3. Donoho, D. L., Huber, P. J. (1983). The notion of breakdown point. In: A Festchrift for Erich L. Lehmann. (Bickel, P. J., Doksum, K. A., Hodges, J. L., eds.) Belmont, CA: Wadsworth, pp. 157-148.
4. Ghosh, A. K., Chaudhuri, P. (2005a). On data depth and distribution free discriminant analysis using separating surfaces. Bernoulli 11:1-27.
5. Ghosh, A. K., Chaudhuri, P. (2005b). On maximum depth and related classifiers. Scand. J. Statist. 32:327-350.
6. 1 data depth. J. Multivariate Anal. 90:67-89.
7. Lin, L. (2005). Robust depth-weighted wavelet for nonparametric regression models. AM. Sinica, English Ser. 21:585-592.
8. Lin, L., Chen, M. H. (2006). Robust estimating equation based on statistical depth. Statist. Pap. 47:263-278.
9. Lin, L., Cui, X. (2006). Stahel-Donoho kernel estimation for fixed design nonparametric regression models. Sci. China. Ser. A. 49(12):1879-1896.
10. Liu, R. Y. (1990). On a notion of data depth based on random simplices. Ann. Statist. 18:405-414.
11. Liu, R. Y., Singh, K. (1993). A quality index based on data depth and multivariate rank tests. J. Amer. Statist. Assoc. 88:252-260.
12. Rousseeuw, P. J., Hubert, M. (1999). Regression depth. J. Amer. Statist. Assoc. 94:389-433.
13. Tukey, J. W. (1975). Mathematics and picturing data. Proc. Intern. Congr. Math. Vancouver 2:523-531.
14. Zuo, Y. J. (2003). Projection-based depth functions and associated medians. Ann. Statist. 31:1460-1490.
15. Zuo, Y. J., Serfling, R. (2000a). General notions of statistical depth function. Ann. Statist. 28:461-482.
16. Zuo, Y. J., Serfling, R. (2000b). Structural properties and convergence results for contours of sample statistical depth functions. Ann. Statist. 28:483-499.
17. Zuo, Y. J., Cui, H. J., He, X. M. (2004). On the Stahel-Donoho estimator and depth-weighed means of multivariate data. Ann. Statist. 32:167-188.