Dimension reduction and visualization in discriminant analysis (with discussion)

Australian and New Zealand Journal of Statistics

Volumn 43, Issue 2, 2001, Pages 147-199

  Cook, R Dennis ^a   Yin, Xiangrong ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSITY OF GEORGIA   (United States)

Author keywords

Central subspaces; Dimension reduction; Regression; Regression graphics; Sliced average variance estimation (SAVE); Sliced inverse regression (SIR)

Indexed keywords

EID: 0012657603     PISSN: 13691473     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-842X.00164     Document Type: Article

References (26)

1. BRIEMAN, L., FRIEDMAN, J., OLSHEN, R. & STONE, C. (1984). Classification and Regression Trees. Belmont, CA: Wadsworth.
2. BROWN, P.L., FEARN, T. & HAQUE, M.S. (1999). Discrimination with many variables. J. Amor. Statist. Assoc. 94, 1320-1329.
3. CHANG, W-C. (1987). A graph for two training samples in a discriminant analysis. Appl. Statist. 36, 82-91.
4. COOK, R.D. (1994a). On the interpretation of regression plots. J. Amer. Statist. Assoc. 89, 177-190.
5. COOK, R.D. (1994b). Using dimension-reduction subspaces to identify important inputs in models of physical systems. In 1994 Proceedings of the Section on Physical Engineering Sciences, pp. 18-25. Alexandria, Virginia: The American Statistical Association.
6. COOK, R.D. (1996). Graphics for regressions with a binary response. J. Amer. Statist. Assoc. 91, 983-992.
7. COOK, R.D. (1998). Regression Graphics: Ideas for Studying Regressions Through Graphics. New York: Wiley.
8. COOK, R.D. (2000). SAVE: A method for dimension reduction and graphics in regression. Comm. Statist. Theory Methods 29, 2109-2121.
9. COOK, R.D. & CRITCHLEY, F. (2000). Identifying outliers and regression mixtures graphically. J. Amer. Statist. Assoc. 95, 781-794.
10. COOK, R.D. & LEE, H. (1999). Dimension reduction in regressions with a binary response. J. Amer. Statist. Assoc. 94, 1187-1200.
11. COOK, R.D. & NACHTSHEIM, C. J. (1994). Re-weighting to achieve elliptically contoured covariates in regression. J. Amer. Statist. Assoc. 89, 592-599.
12. COOK, R.D. & WEISBERG, S. (1991). Discussion of Li (1991). J. Amer. Statist. Assoc. 86, 328-332.
13. COOK, R.D. & WELSBERG, S. (1999). Applied Regression Including Computing and Graphics. New York: Wiley.
14. DAWID, A.P. (1979). Conditional independence in statistical theory (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 41, 1-31.
15. DIACONIS, P. & FREEDMAN, D. (1984). Asymptotics of graphical projection pursuit. Ann. Statist. 12, 793-815.
16. EATON, M. (1986). A characterization of spherical distributions. J. Multivariate Anal. 20, 272-276.
17. ESLAVA-GOMEZ, G. & MARRIOTT, F.H.C. (1993). Criteria to represent groups in the plane when grouping is known. Biometrics 49, 1088-1098.
18. FISHER, R.A. (1936). The use of multiple measurements in taxonomic problems. Ann. Eugenics 7, 179-188.
19. FISHER, R.A. (1938). The statistical utilization of multiple measurements. Ann. Eugenics 8, 376-386.
20. FISHER, R.A. (1940). The precision of discriminant functions. Ann. Eugenics 10, 422-429.
21. FLURY, B. & RIEDWYL, H. (1988). Multivariate Statistics: A Practical Approach. London: Chapman and Hall.
22. FLURY, L., BOUKAI, B. & FLURY, B. (1997). The discrimination subspace model. J. Amer. Statist. Assoc. 92, 758-766.
23. FORINA, M., ARMANINO, C., CASTINO, M. & UBIGLI, M. (1986). Multivariate data analysis as a discriminating method of the origin of wines. Vitis 25, 189-201.
24. GNANADESIKAN, R. (1977). Methods for Statistical Data Analysis of Multivariate Observations. New York: Wiley.
25. GNANADESIKAN, R. (1989). Discriminant analysis and clustering. Statist. Sci. 4, 34-69.
26. HALL, P. & LI, K.C. (1993). On almost linearity of low dimensional projections from high dimensional data. Ann. Statist. 21, 867-889.