Resampling methods for homogeneity tests of covariance matrices

Statistica Sinica

Volumn 12, Issue 3, 2002, Pages 769-783

  Zhu, Li Xing ^a   Ng, Kai W ^a   Jing, Ping ^a  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Bartlett homogeneity test; Bootstrap; Non parametric tests; Permutation test; Random symmetrization

Indexed keywords

EID: 0036661096     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. Anderson, T.W. (1984). An Introduction to Multivariate Statistical Analysis. John Wiley, New York.
2. Beran, R. and Srivastava, M.S. (1985). Bootstrap tests and confidence regions for functions of a covariance matrix. Ann. Statist. 13, 95-115.
3. Boos, D.D. and Brownie, C. (1989). Bootstrap methods for testing homogeneity of variances. Technometrics 31, 69-82.
4. Box, G.E.P. (1949). A general distribution theory for a class of likelihood criteria. Biometrika 36, 317-346.
5. Dunnett, C.W. (1994). Recent results in multiple testing: Several treatments vs. a specified treatment. Proceedings of the International Conference on Linear Statistical Inference LINSTAT'93, Math. Appl. 306, 317-346. Kluwer Acad. Publ., Dordrecht, The Netherlands.
6. 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. Ann. Statist. 19, 260-271.
7. Efron, B. (1979). Bootstrap methods: Another look at the Jackknife. Ann. Statist. 7, 1-26.
8. Giné, E. and Zinn, J. (1984). On the central limit theorems for empirical processes (with discussion). Ann. Probab. 12, 929-998.
9. Giné, E. and Zinn, J. (1990). Bootstrapping general empirical measures. Ann. Probab. 18, 851-869.
10. Jing, P. and Zhu, L.X. (1996). Some Blum-Kiefer-Rosenblatt type tests for the joint independence of variables. Comm. Statist. Theory Methods 25, 2127-2139.
11. Korin, B.P. (1968). On the distribution of a statistic used for testing a covariance matrix. Biometrika 55, 171-178.
12. Muirhead, R.J. (1982). Aspect of Multivariate Statistical Theory. John Wiley, New York.
13. Neuhaus, G. and Zhu, L.X. (1998). Permutation test for reflected symmetry. J. Multivariate Anal. 67, 129-153.
14. O'Brien, R.D. (1979). A general ANOVA method for robust tests for aditive models for variances. J. Amer. Statist. Assoc. 74, 877-880.
15. O'Brien, R.D. (1981). A simple test for variance effects in experimental designs. Psychological Bulletin 89, 570-574.
16. Pearson, E.S. and Hartley, H.O. (1972). Biometrika Tables for Statisticians, Vol. 2. Cambridge University Press, Cambridge.
17. Pollard, D. (1984). Convergence of Stochastic Processes. Springer-Verlag, New York.
18. Praestgaard, J.P. (1995). Permutation and bootstrap Kolmogorov-Smirnov test for the equality of two distributions. Scand. J. Statist. 22, 305-322.
19. Roy, S.N. (1953). On a heuristic method of test construction and its use in Multivariate analysis. Ann. Math. Stat. 24, 220-238.
20. Zhang, J. and Boos, D.D. (1992). Bootstrap critical values for testing homogeneity of covariance matrices. J. Amer. Statist. Assoc. 87, 425-429.
21. Zhang, J. and Boos, D.D. (1993). Testing hypothesis about covariance matrices using bootstrap methods. Comm. Statist. Theory Methods. 22, 723-739.
22. Zhang, J., Pantula, S.G. and Boos, D.D. (1991). Robust methods for testing the pattern of a single covariate matrix. Biometrika 78, 787-795.