Transformed partial least squares for multivariate data

Statistica Sinica

Volumn 17, Issue 4, 2007, Pages 1657-1675

  Li, Xin ^a,c   Zhu, Li Xing ^a   Zhu, Li Ping ^a,b  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b EAST CHINA NORMAL UNIVERSITY   (China)

^c BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Agricultural meteorology; Canonical correlation analysis; Dimension reduction; Model selection; Partial least squares regression; Sliced inverse regression; Spline; Transformation

Indexed keywords

EID: 38549106740     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. Breiman, L. and Friedman, J. H. (1985). Estimating optimal transformations for multiple regression and correlation. J. Amer. Statist. Assoc. 80, 580-598.
2. Bura, E. and Cook, D. (2001). Estimating the structural dimension of regression via parametric inverse regression. J. Roy. Statist. Soe. Ser. B 63, 393-410.
3. Cook, R. D. (1998). Regression Graphics: Ideas for Studying Regressions through Graphics, Wiley, New York.
4. Cook, R. D. and Li, B. (2002). Dimension reduction for the conditional mean in regression. Ann. Statist. 30, 455-474.
5. Cook, R. D. and Setodji, C. M. (2003). A model-free test for reduced rank in multivariate regression. J. Amer. Statist. Assoc. 98, 340-351.
6. Cook, D. and Weisberg, S. (1994). Transforming a response variable for linearity, Biometrika 81, 731-737.
7. Doksùm, K. A. (1987). An extension of partial likelihood methods for proportional hazard models to general transformation models. Ann. Statist. 15, 325-345
8. Friedman, J. H. and Stuetzle, W. (1981). Projection pursuit regression, J. Amer. Statist. Assoc. 76, 817-823.
9. p in multivariate linear regression. Biometrika 84, 707-716.
10. Fung, W. K., He, X., Liu, L. and Shi, P. (2002). Dimension reduction based on canonical correlation. Statist. Sinica 12, 1093-1113.
11. Györfi, L., Kohler, M., Krzyźak, A. and Walk, H. (2002) A Distribution-Free Theory of Nonparametric Regression. Springer, New York.
12. Hall, P. (1989). On projection pursuit regression. Ann. Statist. 17, 573-588.
13. He, X. and Shen, L. (1997). Linear regression after spline transformation. Biometrika 84, 474-481.
14. Huber, P. J. (1985). Projection pursuit (with discussion). Ann. Statist. 13, 435-475.
15. Li, K. C. (1991). Sliced inverse regression for dimension reduction (with discussion). J. Amer. Statist. Assoc. 86, 316-342.
16. 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.
17. Li, K. C. and Duan, N. H. (1989). Regression analysis under link violation. Ann. Statist. 17, 1009-1052.
18. Li, K. C., Aragon Y., Shedden, K., and Agnan, C. T. (2003). Dimension reduction for multivariate response data. J. Amer. Statist. Assoc. 98, 99-109.
19. Li, X. (1999). Quantatitive Definition and Division of Meteorological Disaster in Ji-Lin Province. Masters degree Thesis, Northwest Normal University, Ji-Lin province, China.
20. Ma, S. Q. (1996). The Study on Agriculture Climate in Ji-Lin Province. Meteorology Press, Beijing.
21. McQuarrie, A. D. R. and Trai, C. L. (1998). Regression and Time Series Model Selection. World Scientific, Singapore.
22. Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist. 6, 461-464.
23. Ramsay, J. O. (1988). Monotone regression spline in action (with discussion). Statist. Sci. 3, 425-461.
24. Schumaker, L. L. (1981). Spline Functions. Wiley, New York.
25. Tenehaus, M. (1998). La Régression PLS: Théorie et Pratique. Éditons Technip, Paris, (in French)
26. Xia, Y., Li, W. K., Tong, H. and Zhu, L. X. (2000). On the estimation of an instantaneous transformation for time series, J. Roy. Statist. Soe. Ser. B 62, 283-297.
27. Yin, X. and Bura, E. (2006). Moment based dimension reduction for multivariate response regression. J. Statist. Plann. Inference 136, 3675-3688.
28. Yin, X. and Cook, R. D. (2002). Dimension reduction for the conditional kth moment in regression. J. Roy. Statist. Soc. Ser. B 64, 159-175.
29. Yin, X. and Cook, R. D. (2003). Estimating the central subspace via inverse third moment. Biometrika 90, 113-125.
30. Yin, X. and Cook, R. D. (2004). Dimension reduction via marginal fourth moments in regression. J. Comput. Graph. Statist. 13, 554-570.
31. Yin, X. and Zhu, L. X. (2004). On estimation for dual central subspaces in dimension reduction. Submitted.
32. Zhu, L. X. and Fang, K. T. (1992). On Projection Pursuit approximation for nonparametric regression. In Proceedings of Order Statistics and Nonparametric: Theory and applications (Edited by P. K. Sen and A. I. Salama), 455-469. Elsevier Science Publishers.