Can sir be as popular as multiple linear regression?

Statistica Sinica

Volumn 8, Issue 2, 1998, Pages 289-316

  Chen, Chun Houh ^a   Li, Ker Chau ^b  

^a INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Dimension reduction; Dynamic graphics; Inverse regression; Projection pursuit; Transformation

Indexed keywords

EID: 0032367227     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (41)

1. Bickel, P. J. and Doksum, K. A. (1981). An analysis of transformations revisited. J. Amer. Stat. Assoc. 76, 296-311.
2. Box, G. E. and Cox, D. R. (1964). An analysis of transformations. J. Roy. Statist. Soc. Ser. B 26, 211-252.
3. Breiman, L. and Friedman, J. (1985). Estimating optimal transformations for multiple regression and correlation. (with discussion). J. Amer. Stat. Assoc. 80, 580-619.
4. Breiman, L., Friedman, J., Olshen, R. and Stone, C. (1984). Classification and Regression Trees. CA: Wadsworth.
5. Brillinger, D. R. (1977), The identification of a particular nonlinear time series system. Biometrika 64, 509-515.
6. Brillinger, D. R. (1983). A generalized linear model with 'Gaussian' regressor variables. In A Festschrift for Erich L. Lehmann (Edited by Peter J. Bickel, Kjell A. Doksum and J. L. Hodges, Jr.), 97-114. Wadsworth, Belmont CA.
7. Brillinger, D. R. (1991). Comments on "Sliced inverse regression for dimension reduction". by K. C. Li. J. Amer. Stat. Assoc. 86, 333-333.
8. Carroll, R. J. and Li, K. C. (1992). Measurement error regression with unknown link: Dimension reduction and data visualization. J. Amer. Stat. Assoc. 87, 1040-1050.
9. Carroll, R. and Ruppert, D. (1988). Transformation and Weighting in Regression. Chapman & Hall. London.
10. Carroll, R. J., Wu, C. F. and Ruppert, D. (1988). The effect of estimating weights in weighted least squares. J. Amer. Stat. Assoc. 83, 1045-1054.
11. Chaudhuri, P., Huang, M. C., Loh, W. Y. and Yao, R. (1994). Piecewise-polynomial regression trees. Statist. Sinica 4, 143-167.
12. Chen, H. (1991). Estimation of a projection-pursuit type regression model. Ann. Statist. 19, 142-157.
13. Cook, R. D. (1994). On the interpretation of regression plots. J. Amer. Stat. Assoc. 89, 177-189.
14. Cook, R. D., Hawkins, D. M. and Weisberg, S. (1992). Comparison of model misspecification diagnostics using residuals from least mean of squares and least median of squares fits. J. Amer. Stat. Assoc. 87, 419-424.
15. Cook, R. D. and Nachtsheim, C. J. (1994). Reweighting to achieve elliptically contoured covariates in regression. J. Amer. Statist. Assoc. 89, 592-599.
16. Cook, R. D. and Weisberg, S. (1991). Comment on "Sliced inverse regression for dimension reduction". by K. C. Li. J. Amer. Stat. Assoc. 86, 328-332.
17. Cook, R. D. and Wetzel, N. (1994). Exploring regression structure with graphics. (with discussion). Test 2, 33-100.
18. de Leeuw, J. (1981). The GIFI-system of nonlinear multivariate analysis. In Data Analysis and Informatics III (Edited by E. Diday, M. Jambu, L. Lebart, J. Pages and R. Tomassone), 415-424. North Holland, Amsterdam.
19. Diaconis, P. and Freedman, D. (1984). Asymptotics of graphical projection pursuit. Ann. Statist. 12, 793-815.
20. Duan, N. and Li, K. C. (1991). Slicing regression : a link-free regression method. Ann. Statist. 19, 505-530.
21. Friedman, J. H. and Stuetzle, W. (1981). Projection pursuit regression. J. Amer. Statist. Assoc. 76, 817-823.
22. Friedman, J. H. (1990). Multivariate adaptive regression splines. (with discussion). Ann. Statist. 19, 1-141.
23. Gifi, A. (1990). Nonlinear Multivariate Analysis. John Wiley, Chichester.
24. Hall, P. (1989). On projection pursuit regression. Ann. Statist. 17, 573-588.
25. Hall, P. and Li, K. C. (1993). On Almost linearity of low dimensional projections from high dimensional data. Ann. Statist. 21, 867-889.
26. Harrison, D. and Rubinfeld, D. L. (1978). Hedonic housing prices and the demand for clean air. J. Environmental Economics Management 5, 81-102.
27. Hinkley, D. V. and Runger, G. (1984). The analysis of transformed data. (with discussion). J. Amer. Statist. Assoc. 79, 302-320.
28. Hsing, T. and Carroll, R. J. (1992). An asymptotic theory for sliced inverse regression. Ann. Statist. 20, 1040-1061.
29. Huber, P. J. (1985). Projection pursuit. (with discussion). Ann. Statist. 13, 435-525.
30. Knickerbocker, R. K., Wang, C. Y. and Carroll, R. J. (1992). Dimension reduction in a semiparametric regression model with errors in covariates. Manuscript.
31. Koyak, R. A. (1987). On measuring internal dependence in a set of random variables. Ann. Statist. 15, 1215-1228.
32. Li, K. C. (1990). Data visualization with SIR: a transformation-based projection pursuit method. UCLA Statist Ser. 24.
33. Li, K. C. (1991). Sliced inverse regression for dimension reduction. (with discussion). J. Amer. Statist. Assoc. 86, 316-342.
34. Li, K. C. (1992a). Uncertainty analysis for mathematical models with SIR. In Probability and Statistics (Edited by Z. P. Jiang, S. J. Yan, P. Cheng and R. Wu), 138-162. World Scientific, Singapore.
35. Li, K. C. (1992b). On principal hessian directions for data visualization and dimension reduction: Another application of stein's lemma. J. Amer. Statist. Assoc. 87, 1025-1039.
36. Li, K. C. (1997). Nonlinear confounding in high-dimensional regression. Ann. Statist. 25, 577-612.
37. Li, K. C. and Duan, N. (1989). Regression analysis under link violation. Ann. Statist. 17, 1009-1052.
38. Schott, J. R. (1994). Determining the dimensionality in sliced inverse regression. J. Amer. Statist. Assoc. 89, 141-148.
39. Tierney, L. (1990). LISP-STAT: An Object-Oriented Environment for Statistical Computing and Dynamic Graphics. John Wiley, New York.
40. Zhu, L. X. and Fang, K. T. (1996). Asymptotics for kernel estimate of sliced inverse regression. Ann. Statist. 24, 1053-1068.
41. Zhu, L. X. and Ng, K. W. (1995). Asymptotics of sliced inverse regression. Statist. Sinica 5, 727-736.