A model-free test for reduced rank in multivariate regression

Journal of the American Statistical Association

Volumn 98, Issue 462, 2003, Pages 340-351

  Cook, R Dennis ^a   Setodji, C Messan ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b RAND CORPORATION   (United States)

Author keywords

Central subspaces; Dimension reduction; Multivariate regression; Regression; Regression graphics

Indexed keywords

EID: 0041743092     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214503000134     Document Type: Article

References (27)

1. Anderson, T. W. (1951), "Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distribution," Annals of Mathematical Statistics, 22, 327-351.
2. _ (1999a), "Asymptotic Distribution of the Reduced Rank Regression Estimator Under General Conditions," The Annals of Statistics. 27, 1155-1163.
3. _ (1999b), "Asymptotic Theory for Canonical Correlation Analysis," Journal of Multivariate Analysis, 70, 1-29.
4. Barlett, M. S. (1947), "Multivariate Analysis," Journal of the Royal Statistical Society, Ser. B, 9, 176-U″197.
5. Bentler, P. M., and Xie, J. (2000), "Corrections to Test Statistics in Principal Hessian Direction," Statistics and Probability Letters, 47, 381-389.
6. Bura, E., and Cook, R. D. (2002), "Rank Estimation in Reduced Rank Regression," Submitted.
7. Cook, D., Buja, A., and Cabrera, J. (1993), "Projection Pursuit Indices Based on Orthonormal Function Expansions," Journal of Computational and Graphical Statistics, 2, 225-250.
8. Cook, R. D. (1998), Regression Graphics, New York: Wiley.
9. Cook, R. D., and Li, B. (2002), "Dimension Reduction for Conditional Mean in Regression," The Annals of Statistics, 30, 455-474.
10. Cook, R. D., and Nachtsheim, C. J. (1994), "Reweighting to Achieve Elliptically Contoured Covariates in Regression," Journal of the American Statistical Association, 89, 592-600.
11. Davison, A. C., and Hinkley, D. V. (1997), Bootstrap Methods and Their Application, Cambridge, UK. Cambridge University Press.
12. Diaconis, P., and Freedman, D. (1984), "Asymptotics of Graphical Projection Pursuit," The Annals of Statistics, 12, 793-815.
13. Eaton, M. L., and Tyler, D. (1994), "The Asymptotic Distribution of Singular Values With Application to Canonical Correlations and Correspondence Analysis," Journal of Multivariate Analysis, 50, 238-264.
14. Efron, B., and Tibshirani, R. J. (1993), An Introduction to the Bootstrap, New York: Chapman and Hall.
15. 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.
16. Fouladi, R. T. (1997), "Type I Error Control of Some Covariance Structure Analysis Technique Under Conditions of Multivariate Non-Normality," Computing Science and Statistics, 29, 526-532.
17. Hall, P., and Li, K. C. (1993), "On Almost Linearity of Low-Dimensional Projections From High-Dimensional Data," The Annals of Statistics, 21, 867-889.
18. Hirstache, M., Juditsky, A., and Spokoiny, V. (2001), "Direct Estimation of the Index Coefficients in a Single-Index Model," The Annals of Statistics, 29, 595-623.
19. Ichimura, H. (1993), "Semiparametric Least Squares (SLS) and Weighted SLS Estimation of Single-Index Models," Journal of Econometrics, 58, 71-120.
20. Izenman, A. L. (1975), "Reduced-Rank Regression for Multivariate Linear Models," Journal of Multivariate Analysis, 5, 248-264.
21. Li, B., Cook, R. D., and Chiarmonte, F. (2003), "Dimension Reduction for the Conditional Mean in Regressions With Categorical Predictors," The Annals of Statistics, to appear.
22. 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, 1025-1040.
23. Reinsel, G. C., and Velu, R. P. (1998), Multivariate Reduced-Rank Regression, New York: Springer.
24. Satterthwaite, F. E. (1941), "Synthesis of Variance," Psychometrika, 6, 309-316.
25. Schmidli, H. (1996), Reduced-Rank Regression, Berlin: Physica.
26. Stocker, T. M. (1986), "Consistent Estimation of Scaled Coefficients," Econometrica, 54, 1461-1481.
27. Velilla, S. (1998), "Assessing the Number of Linear Components in a General Regression Problem," Journal of the American Statistical Association, 93, 1088-1098.