Contour projected dimension reduction

Annals of Statistics

Volumn 37, Issue 6 B, 2009, Pages 3743-3778

  Luo, Ronghua ^a,b   Wang, Hansheng ^a,c   Tsai, Chih Ling ^a,d  

^a SOUTHWESTERN UNIVERSITY   (United States)

^b SOUTHWESTERN UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^c Peking University   (China)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

n Consistency; Central contour subspace; Central subspace; Contour projection; Directional regression; Generalized contour subspace; Kernel contour subspace; Sliced average variance estimation; Sliced inverse regression; Sufficient contour subspace

Indexed keywords

EID: 73149086049     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS679     Document Type: Article

References (37)

1. CHIAROMONTE, F., COOK, R. D. and LI, B. (2002). Partial dimension reduction with categorical predictors. Ann. Statist. 30 475-497. MR1902896
2. COOK, R. D. (1994). On interpretation of regression plots. J. Amer. Statist. Assoc. 89 177-189. MR1266295
3. COOK, R. D. (1996). Graphics for regression with a binary response. J. Amer. Statist. Assoc. 91 983-992. MR1424601
4. COOK, R. D. (1998a). Principal Hessian directions revisited. J. Amer. Statist. Assoc. 93 84-94. MR1614584
5. COOK, R. D. (1998b). Regression Graphics. Wiley, New York. MR1645673
6. COOK, R. D. and LEE, H. (1999). Dimension reduction in binary response regression. J. Amer. Statist. Assoc. 94 1187-1200. MR1731482
7. COOK, R. D. and NACHTSHEIM, C. J. (1994). Reweighting to achieve elliptically contoured covariates in regression. J. Amer. Statist. Assoc. 89 592-599.
8. COOK, R. D. and NI, L. (2005). Sufficient dimension reduction via inverse regression: A minimum discrepancy approach. J. Amer. Statist. Assoc. 100 410-428. MR2160547
9. COOK, R. D. and SETODJI, M. (2003). A model free test for reduced rank in multivariate regression. J. Amer. Statist. Assoc. 98 340-351. MR1995710
10. COOK, R. D. and WEISBERG, S. (1991). Discussion of "Sliced inverse regression for dimension reduction. " J. Amer. Statist. Assoc. 86 28-33. MR1137117
11. EATON, M. L. (1986). A characterization of spherical distribution. J. Multivariate Anal. 20 272-276. MR0866075
12. EATON, M. L. and TYLER, D. (1994). The asymptotic distribution of singular values with applications to canonical correlations and correspondence analysis. J. Multivariate Anal. 50 238-264. MR1293045
13. JIANG, G. and WANG, H. (2008). Should earnings thresholds be used as delisting criteria in stock market? J. Accounting and Public Policy 27 409-419.
14. LANGE, K. L., LITTLE, R. J. A. and TAYLOR, J. M. G. (1989). Robust statistical modeling using t distribution. J. Amer. Statist. Assoc. 84 881-896. MR1134486
15. LI, K.-C. (1991). Sliced inverse regression for dimension reduction. J. Amer. Statist. Assoc. 86 316-327. MR1137117
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. MR1209564
17. 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. MR1965677
18. LI, K.-C. and DUAN, N. (1989). Regression analysis under link violation. Ann. Statist. 17 1009-1052. MR1015136
19. LI, B. and WANG, S. (2007). On directional regression for dimension reduction. J. Amer. Statist. Assoc. 102 997-1008. MR2354409
20. LI, B., WEN, S. and ZHU, L. (2008). On a projective re-sampling method for dimension reduction with multivariate responses. J. Amer. Statist. Assoc. 103 1177-1186. MR2462891
21. LI, B., ZHA, H. and CHIAROMONTE, F. (2005). Contour regression: A general approach to dimension reduction. Ann. Statist. 33 1580-1616. MR2166556
22. LI, Y. X. and ZHU, L. (2007). Asymptotics for sliced average variance estimation. Ann. Statist. 35 41-69. MR2332268
23. MUIRHEAD, R. J. (1982). Aspects of Multivariate Statistical Theory. Wiley, New York. MR0652932
24. NI, L., COOK, R. D. and TSAI, C. L. (2005). A note on shrinkage sliced inverse regression. Biometrika 92 242-247. MR2158624
25. SHAO, Y., COOK, R. D. and WEISBERG, S. (2007). Marginal test with sliced average variance estimation. Biometrika 94 285-296. MR2331487
26. TYLER, D. E. (1987). A distribution-free M-estimator of multivariate scatter. Ann. Statist. 15 234-251. MR0885734
27. WANG, H., NI, L. and TSAI, C. L. (2008). Improving dimension reduction via contour projection. Statist. Sinica 18 299-311.
28. WANG, H. and XIA, Y. (2008). Sliced regression for dimension reduction. J. Amer. Statist. Assoc. 103 811-821.
29. XIA, Y. (2007). A constructive approach to the estimation of dimension reduction directions. Ann. Statist. 35 2654-2690. MR2382662
30. XIA, Y., TONG, H., LI, W. K. and ZHU, L. (2002). An adaptive estimation of dimension reduction space. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 363-410. MR1924297
31. YE, Z. and WEISS, R. E. (2003). Using the bootstrap to selection one of a new class of dimension reduction methods. J. Amer. Statist. Assoc. 98 968-979. MR2041485
32. YIN, X. and COOK, R. D. (2002). Dimension reduction for the conditional kth moment in regression. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 159-175. MR1904698
33. YIN, X. and COOK, R. D. (2003). Estimating central subspace via inverse third moment. Biometrika 90 113-125. MR1966554
34. YIN, X. and COOK, R. D. (2004). Dimension reduction via marginal fourth moments in regression. J. Computat. Graph. Statist. 13 554-570. MR2087714
35. ZENG, P. and ZHU, Y. (2008). An integral transformation method for estimating the central mean and central subspaces. Unpublished manuscript.
36. ZHU, L. and FANG, K. T. (1996). Asymptotics for kernel estimates of sliced inverse regression. Ann. Statist. 24 1053-1068. MR1401836
37. ZHU, Y. and ZENG, P. (2006). Fourier methods for estimating the central subspace and the central mean subspace in regression. J. Amer. Statist. Assoc. 101 1638-1651. MR2279485