On kernel method for sliced average variance estimation

Journal of Multivariate Analysis

Volumn 98, Issue 5, 2007, Pages 970-991

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

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

Asymptotic normality; Bandwidth selection; Dimension reduction; Kernel estimation; Sliced average variance estimation; Sliced inverse regression; Slicing estimation

Indexed keywords

EID: 33947148667     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2006.11.005     Document Type: Article

References (27)

1. Bura E., and Cook R.D. Estimating the structural dimension of regressions via parametric inverse regression. J. Roy. Statist. Soc. B. 63 (2001) 393-410
2. Carroll R.J., Fan J., Gijbels I., and Wand M.P. Generalized partially linear single-index models. J. Amer. Statist. Assoc. 92 (1997) 477-489
3. Cook R.D. On the interpretation of regression plots. J. Amer. Statist. Assoc. 89 (1994) 177-189
4. Cook R.D. Regression Graphics: Ideas for Studying Regressions through Graphics (1998), Wiley, New York
5. Cook R.D. SAVE: a method for dimension reduction and graphics in regression. Comm. Statist. Theory Methods 29 (2000) 2109-2121
6. Cook R.D., and Critchley F. Identifying regression outliers and mixtures graphically. J. Amer. Statist. Assoc. 95 (2000) 781-794
7. Cook R.D., and Weisberg S. Discussion to "Sliced inverse regression for dimension reduction". J. Amer. Statist. Assoc. 86 (1991) 316-342
8. Fearn T. A misuse of ridge regression in the calibration of near infrared reflectance instruments. Appl. Statist. 32 (1983) 73-79
9. Ferre L. Determining the dimension in sliced inverse regression and related methods. J. Amer. Statist. Assoc. 93 (1998) 132-140
10. Härdle W., and Mammen E. Comparing nonparametric versus parametric regression fits. Ann. Statist. 21 (1993) 1926-1947
11. Hsing T., and Carroll R.J. An asymptotic theory for sliced inverse regression. Ann. Statist. 20 (1992) 1040-1061
12. Li K.C. Sliced inverse regression for dimension reduction (with discussion). J. Amer. Statist. Assoc. 86 (1991) 316-342
13. Li B., Zha H., and Chiaromonte F. Contour regression: a general approach to dimension reduction. Ann. Statist. 33 (2005) 1580-1616
14. Y.X. Li, L.X. Zhu, When is sliced average variance estimation convergent? Technical Report, Department of Statistics and Actuarial Science, The University of Hong Kong. Hong Kong, 2004.
15. Schott J.R. Determining the dimensionality in sliced inverse regression. J. Amer. Statist. Assoc. 89 (1994) 141-148
16. Schwarz G. Estimating the dimension of a model. Ann. Math. Statist. 30 (1978) 461-464
17. Stute W., and Zhu L.X. Nonparametric checks for single-index models. Ann. Statist. 33 (2005) 1048-1083
18. Velilla S. Assessing the number of linear components in a general regression problem. J. Amer. Statist. Assoc. 93 (1998) 1088-1098
19. Ye Z., and Weiss R. Using the bootstrap to select one of a new class of dimension reduction methods. J. Amer. Statist. Assoc. 98 (2003) 968-979
20. Zhao L.C., Krishnaiah P.R., and Bai Z.D. On detection of the number of signals in presence of white noise. J. Multivariate Anal. 20 (1986) 1-25
21. Zhao L.C., Krishnaiah P.R., and Bai Z.D. On detection of the number of signals when the noise covariance matrix is arbitrary. J. Multivariate Anal. 20 (1986) 26-49
22. Zhu L.X. Model checking of dimensional-reduction type for regression. Statist. Sin. 13 (2003) 283-296
23. Zhu L.X., and Fang K.T. Asymptotics for kernel estimate of sliced inverse regression. Ann. Statist. 24 (1996) 1053-1068
24. Zhu L.X., and Ng K.W. Asymptotics of sliced inverse regression. Statist. Sin. 5 (1995) 727-736
25. Zhu L.X., Miao B.Q., and Peng H. Sliced inverse regression with high-dimensional covariates. J. Amer. Statist. Assoc. 101 (2006) 630-643
26. Zhu L.X., and Ng K.W. Checking the adequacy of a partial linear model. Statist. Sin. 13 (2003) 763-781
27. L.X. Zhu, M. Ohtaki, Y.X. Li, Hybrid methods of inverse regression based algorithms, Comp. Statist. Data. Anal. 51 (2007) 2621-2635.