A note on outlier sensitivity of sliced inverse regression

Statistics

Volumn 36, Issue 4, 2002, Pages 271-281

  Gather, Ursula ^a   Hilker, Torsten ^a   Becker, Claudia ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Dimension reduction; Outliers; Robustness

Indexed keywords

EID: 0036934876     PISSN: 02331888     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331880213194     Document Type: Article

References (36)

1. Aragon, Y. and Saracco, J. (1997). Sliced inverse regression (SIR): An appraisal of small sample alternatives to slicing. Comput. Statist., 12, 109-130.
2. Becker, C. and Gather, U. (1999). The masking breakdown point of multivariate outlier identification rules. J. Amer. Statist. Assoc., 94, 947-955.
3. 1-Statistical Procedures and Related Topics, IMS Lecture Notes, 31, pp. 215-228.
4. Carroll, R. J. and Li, K.-C. (1992). Measurement error regression with unknown link: dimension reduction and data visualization. J. Amer. Statist. Assoc., 87, 1040-1050.
5. Chen, C.-H. and Li, K.-C. (1998). Can SIR be as popular as multiple linear regression? Statist. Sinica, 8, 289-316.
6. Chen, C.-H. and Li, K.-C. (2001). Generalization of Fisher's linear discriminant analysis via the approach of sliced inverse regression. J. Korean Statist. Soc., 30, 193-217.
7. Cook, R. D. (1994). On the interpretation of regression plots. J. Amer. Statist. Assoc., 89, 177-189.
8. Cook, R. D. (1996). Graphics for regressions with a binary response. J. Amer. Statist. Assoc., 91, 983-992.
9. Cook, R. D. (1998a). Principal Hessian directions revisited. J. Amer. Statist. Assoc., 93, 84-100.
10. Cook, R. D. (1998b). Regression Graphics: Ideas for Studying Regressions through Graphics. Wiley, New York.
11. Cook, R. D. and Critchley, F. (2000). Identifying regression outliers and mixtures graphically. J. Amer. Statist. Assoc., 95, 781-794.
12. Cook, R. D. and Lee, H. (1999). Dimension-reduction in binary response regression. J. Amer. Statist. Assoc., 94, 1187-1200.
13. Cook, R. D. and Nachtsheim, C. J. (1994). Reweighting to achieve elliptically contoured covariates in regression. J. Amer. Statist. Assoc., 89, 592-599.
14. Cook, R. D. and Weisberg, S. (1991). Comment on "Sliced inverse regression for dimension reduction" by Li, K. C. J. Amer. Statist. Assoc., 86, 328-332.
15. Cook, R. D. and Weisberg, S. (1994). An Introduction to Regression Graphics, Wiley, New York.
16. Cook, R. D. and Yin, X. (2001). Dimension reduction and visualization in discriminant analysis (with discussion). Austral. and New Zeal. J. Statist., 43, 147-199.
17. Ferré, L. (1997). Dimension choice for sliced inverse regression based on ranks. Student, 2, 95-108.
18. Ferré, L. (1998). Determining the dimension in sliced inverse regression and related methods. J. Amer. Statist. Assoc., 93, 132-140.
19. Friedman, J. H. (1991). Multivariate adaptive regression splines, invited paper with discussion. Ann. Statist., 19, 1-141.
20. Friedman, J. H. and Stuetzle, W. (1981). Projection pursuit regression. J. Amer. Statist. Assoc., 76, 817-823.
21. Griffiths, P. and Hill, I. H. (Eds.) (1985). Applied Statistics Algorithms. Royal Statistical Society, Ellis Horwood Limited.
22. Härdle, W. and Tsybakov, A. B. (1991). Comment on "Sliced inverse regression for dimension reduction" by Li, K. C. J. Amer. Statist. Assoc., 86, 333-335.
23. Härdle, W., Klinke, S. and Turlach, B. A. (1995). XploRe: An Interactive Computing Environment. Springer, New York.
24. Hall, P. and Li, K.-C. (1993). On almost linearity of low dimensional projections from high dimensional data. Ann. Statist., 21, 867-889.
25. Hsing, T. (1999). Nearest neighbor inverse regression. Ann. Statist., 27, 697-731.
26. Hsing, T. and Carroll, R. J. (1992). An asymptotic theory for sliced inverse regression. Ann. Statist., 20, 1040-1061.
27. Kötter, T. (1996). An asymptotic result for sliced inverse regression. Comput. Statist., 11, 113-136.
28. Kshirsagar, A. M. (1972). Multivariate Analysis. Marcel Dekker, New York.
29. Li, K.-C. (1991). Sliced inverse regression for dimension reduction (with discussion). J. Amer. Statist. Assoc., 86, 316-342.
30. Li, K.-C. (1992). On principal Hessian directions for data visualization and dimension reduction: another application of Stein's lemma. J. Amer. Statist. Assoc., 87, 1025-1039.
31. Li, K.-C., Wang, J.-L. and Chen, C.-H. (1999). Dimension reduction for censored regression data. Ann. Statist., 27, 1-23.
32. Rocke, D. M. (1996). Robustness properties of S-estimators of multivariate location and shape in high dimension. Ann. Statist., 24, 1327-1345.
33. Saracco, J. (1999). Sliced inverse regression under linear constraints. Comm. Statist. -Theory and Methods, 28, 2367-2393.
34. Schott, J. R. (1994). Determining the dimensionality in sliced inverse regression. J. Amer. Statist. Assoc., 89, 141-148.
35. 1 -Statistical Procedures and Related Topics, IMS Lecture Notes, 31, 271-278.
36. Zhu, L.-X. and Fang, K.-T. (1996). Asymptotics for kernel estimate of sliced inverse regression. Ann. Statist., 24, 1053-1068.