Dimension Reduction in Binary Response Regression

Journal of the American Statistical Association

Volumn 94, Issue 448, 1999, Pages 1187-1200

  Cook, R Dennis ^a   Lee, Hakbae ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b AMERICAN UNIVERSITY   (United States)

Author keywords

Dimension reduction subspace; Linear combinations of chi squared variables; Principal Hessian direction; Regression graphics; Sliced average variance estimation; Sliced inverse regression

Indexed keywords

EID: 0442278036     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1999.10473873     Document Type: Article

References (38)

1. Anderson, J. A. (1975), "Quadratic Logistic Discrimination," Biometrika, 62, 149-154.
2. Bura, E. (1997), "Dimension Reduction via Inverse Regression," in Li-Statistical Procedure and Related Topics, IMS Lecture Notes Monograph Series 31, ed. Y. Dodge, Hayward, CA: Institute of Mathematical Statistics, 215-228.
3. Cook, R. D. (1994a), "On the Interpretation of Regression Plots," Journal of the American Statistical Association, 89. 177-189.
4. Cook, R. D. (1994b), "Using Dimension-Reduction Subspaces to Identify Important Inputs in Models of Physical Systems," in Proceedings of the Section on Physical and Engineering Sciences Section, American Statistical Association, pp. 18-25.
5. Cook, R. D. (1996), "Graphics for Regressions With a Binary Response," Journal of the American Statistical Association, 91. 983-992.
6. Cook, R. D. (1998a), "Principal Hessian Directions Revisited" (with discussion). Journal of the American Statistical Association, 93, 84-100.
7. Cook, R. D. (1998b), Regression Graphics, Ideas for Studying Regressions Through Graphics, New York: Wiley.
8. Cook, R. D., and Nachtsheim, C. J. (1994), "Reweighting to Achieve El-liptically Contoured Covariates in Regression," Journal of the American Statistical Association, 89, 592-599.
9. Cook, R. D., and Weisberg, S. (1991), Discussion of "Sliced Inverse Re-gression" by K. C. Li, Journal of the American Statistical Association, 86. 328-332.
10. Eaton, M. L. (1983), Multivariate Statistics: A Vector Space Approach, New York: Wiley.
11. Eaton, M. L., and Tyler, D. E. (1991), "On Wielandt's Inequality and Its Application to the Asymptotic Distribution of the Eigenvalues of a Random Symmetric Matrix" The Annals of Statistics, 19. 260-271.
12. Eaton, M. L., and Tyler, D. E. (1994) "The Asymptotic Distribution of Singular Values With Applications to Canonical Correlations and Correspondence Analysis." Journal of Multivariate Analysis, 34, 439-446
13. Fabian, V., and Hannan, J. (1985), Introduction to Probability and Mathe-matical Statistics, New York: Wiley.
14. Farebrother, R. W. (1990) "The Distribution of a Quadratic Form in Normal Variables," Applied Statistics, 39, 294-309.
15. Ferre, L. (1997) "Dimension Choice for Sliced Inverse Regression Based on Ranks" Student, 2, 95-108.
16. Field, C. (1993), "Tail Areas of Linear Combinations of Chi-Squares and Non-Central Chi-Squares," Journal of Statistical Computation and Simulation, 45, 243-248.
17. Flury, B., and Riedwyl, H. (1988), Multivariate Statistics: A Practical Approach, London: Chapman and Hall.
18. Gu, C. (1993), "Smoothing Spline Density Estimation: A Dimensionless Automatic Algorithm," Journal of the American Statistical Association, 88. 495-504.
19. Gu, C. (1995), "Smoothing Spline Density Estimation: Conditional Distri-bution." Statistica Sinica, 5, 709-726.
20. Gu, C., and Qiu, C. (1993) "Smoothing Spline Density Estimation: Theory," The Annals of Statistics, 21, 217-234.
21. Gu, C., and Wahba, G. (1993) "Semiparametric Analysis of Variance With Tensor Product Thin Plate." Journal of the Royal Statistical Society, Ser. B, 55, 353-368.
22. Hsing, T., and Carroll, R. J. (1992) "An Asymptotic Theory of Sliced Inverse Regression." The Annals of Statistics. 20, 1040-1061.
23. Kay, R., and Little, S. (1987), 'Transforming the Explanatory Variables in the logistic Regression Model for Binary Data," Biometrika, 74. 495-501.
24. Li, K. C. (1991) "Sliced Inverse Regression for Dimension Reduction" (with discussion), Journal of the American Statistical Association, 86. 316-342.
25. Li, K. C. (1992) "On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma," Journal of the American Statistical Association, 87, 1025-1039.
26. Li, K. C., and Duan, N. (1989) "Regression Analysis Under Link Violation," The Annals of Statistics, 17. 1009-1052.
27. Magnus, J. R., and Neudecker, H. (1979), 'The Commutation Matrix: Some Properties and Applications," The Annals of Statistics, 7, 381-394.
28. Muirhead, R. J. (1982), Aspects of Multivariate Statistical Theory. New York: Wiley.
29. Pillai, K. (1955) "Some New Test Criteria in Multivariate Analysis." Annals of Mathematical Statistics, 26, 117-121.
30. Rao, C. R. (1973) Linear Statistical Inference and Its Applications (2nd ed). New York: Wiley.
31. Seber, G. (1984) Multivariate Observations. New York: Wiley.
32. Smith, J. W., Everhart, J. E., Dickson, W. C., Knowler, W. C., and Johannes, R. S. (1988), "Using the ADAP Learning Algorithm to Forecast the Onset of Diabetes Mellitus," in Proceedings of the Symposium on Computer Applications and Medical Care, New York: IEEE Computer Society Press, pp. 261-265.
33. Stein, C. (1981), "Estimating the Mean of a Multivariate Normal Distribution," The Annals of Statistics, 9, 1135-1151.
34. Tyler, D. E. (1981), "Asymptotic Inference for Eigenvectors," The Annals of Statistics, 9. 725-736.
35. Velilla, S. (1993), "A Note on Multivariate Box-Cox Transformations to Normality," Statistics and Probability Letters, 17. 315-322.
36. Wood, A. T. A. (1989), "An F Approximation to the Distribution of a Linear Combination of Chi-Squared Variables," Communications in Statistics, Part B-Simulation and Computation, 18, 1439-1456.
37. Zhu, L.-X., and Fang, K.-T. (1996) "Asymptotics for Kernel Estimate of Sliced Inverse Regression," The Annals of Statistics, 24, 1053-1068.
38. Zhu, L.-X., and Ng, K.-W. (1995) "Asymptotics of Sliced Inverse Regression." Statistica Sinica, 5, 727-736.