Likelihood-based sufficient dimension reduction

Journal of the American Statistical Association

Volumn 104, Issue 485, 2009, Pages 197-208

  Cook, R Dennis ^a   Forzani, Liliana ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSIDAD NACIONAL DEL LITORAL   (Argentina)

Author keywords

Central subspace; Directional regression; Grassmann manifolds; Sliced average variance estimation; Sliced inverse regression

Indexed keywords

EID: 67649302361     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2009.0106     Document Type: Article

References (20)

1. Bura, E., and Pfeiffer, R. M. (2003), "Graphical Methods for Class Prediction Using Dimension Reduction Techniques on DNA Microarray Data, "Bioinformatics (Oxford, England), 19, 1252-1258.
2. Burnham, K., and Anderson, D. (2002), Model Selection and Multimodel Inference, New York: Wiley.
3. Chikuse, Y. (2003), Statistics on Special Manifolds, New York: Springer.
4. Cook, R. D. (1994), "Using Dimension-Reduction Subspaces to Identify Important Inputs in Models of Physical Systems," in Proceedings of the Section on Physical and Engineering Sciences, Alexandria, VA: American Statistical Association, pp. 18-25.
5. - (1998), Regression Graphics, New York: Wiley.
6. Cook, R. D., and Ni, L. (2005), "Sufficient Dimension Reduction via Inverse Regression: A Minimum Discrepancy Approach, "Journal of the American Statistical Association, 100, 410-428.
7. Cook, R. D., and Weisberg, S. (1991), "Discussion of Sliced Inverse Regression" by K. C. Li, Journal of the American Statistical Association, 86, 328-332.
8. Cook, R. D., and Yin, X. (2001), "Dimension Reduction and Visualization in Discriminant Analysis" (with discussion), Australia New Zealand Journal of Statistics, 43, 147-199.
9. Diaconis, P., and Freedman, D. (1984), "Asymptotics of Graphical Projection Pursuit, "The Annals of Statistics, 12, 793-815.
10. Li, L., and Li, H. (2004), "Dimension Reduction Methods for Microarrays With Application to Censored Survival Data, "Bioinformatics, (Oxford, England), 20, 3406-3412.
11. Li, B., and Wang, S. (2007), "On Directional Regression for Dimension Reduction, "Journal of the American Statistical Association, 102, 997-1008.
12. Li, K. C. (1991), "Sliced Inverse Regression for Dimension Reduction" (with discussion), Journal of the American Statistical Association, 86, 316-342.
13. Pardoe, I., Yin, X., and Cook, R. D. (2007), "Graphical Tools for Quadratic Discriminant Analysis, "Technometrics, 49, 172-183.
14. Rao, C. R. (1973), Linear Statistical Inference and Its Applications (2nd ed.), New York: Wiley.
15. Shao, Y., Cook, R. D., and Weisberg, S. (2007), "Marginal Tests With Sliced Average Variance Estimation, "Biometrika, 94, 285-296.
16. Shapiro, A. (1986), "Asymptotic Theory of Overparameterized Structural Models, "Journal of the American Statistical Association, 81, 142-149.
17. Small, C. G., Wang, J., and Yang, Z. (2000), "Eliminating Multiple Root Problems in Estimation, "Statistical Science, 15, 313-332.
18. Ye, Z., and Weiss, R. (2003), "Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods, "Journal of the American Statistical Association, 98, 968-978.
19. Zhu, L., Ohtaki, M., and Li, Y. (2005), "On Hybrid Methods of Inverse Regression-Based Algorithms, "Computational Statistics & Data Analysis, 51, 2621-2635.
20. Zhu, M., and Hastie, T. J. (2003), "Feature Extraction for Nonparametric Discriminant Analysis, "Journal of Computational and Graphical Statistics, 12, 101-120.