Conditional tests for elliptical symmetry

Journal of Multivariate Analysis

Volumn 84, Issue 2, 2003, Pages 284-298

  Zhu, Li Xing ^a   Neuhaus, Georg ^b  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF HAMBURG   (Germany)

Author keywords

Conditional test; Elliptical symmetry; Empirical process; Validity of test

Indexed keywords

EID: 0037299606     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0047-259X(02)00036-2     Document Type: Review

References (19)

1. L. Baringhaus, Testing for spherical symmetry of a multivariate distribution, Ann. Statist. 19 (1991) 899-917.
2. L. Baringhaus, N. Henze, Limit distributions for measures of skewness and kurtosis based on projections, J. Multivariate Anal. 38 (1991) 51-69.
3. R. Beran, Testing for ellipsoidal symmetry of a multivariate density, Ann. Statist. 7 (1979) 150-162.
4. J. Besag, P.J. Diggle, Simple Monte Carlo tests for spatial pattern, Appl. Statist. 26 (1977) 327-333.
5. D.K. Blough, Multivariate symmetry via projection pursuit, Ann. Inst. Statist. Math. 41 (1989) 461-475.
6. A.P. Dempster, Elements of Continuous Multivariate Analysis, Addison-Wesley, Reading, MA, 1969.
7. C. Diks, H. Tong, A test for symmetries of multivariate probability distributions, Biometrika 86 (1999) 605-614.
8. S. Engen, M. Lillegård, Stochastic simulations conditioned on sufficient statistics, Biometrika 84 (1997) 235-240.
9. K.T. Fang, L.X. Zhu, P.M. Bentler, A necessary test of goodness of fit for sphericity, J. Multivariate Anal. 44 (1993) 34-55.
10. J.H. Friedman, Exploratory projection pursuit, J. Amer. Statist. Assoc. 82 (1987) 249-266.
11. S. Ghosh, F.H. Ruymgaart, Applications of empirical characteristic functions in some multivariate problem, Canad. J. Statist. 20 (1992) 429-440.
12. T. Kariya. M.L. Eaton, Robust tests for spherical symmetry, Ann. Statist. 1 (1977) 206-215.
13. K.C. Li, Sliced inverse regression for dimension reduction (with discussions), J. Amer. Statist. Assoc. 85 (1991) 316-342.
14. R.Z. Li, K.T. Fang, L.X. Zhu, Some Q-Q probability plots to test spherical and elliptical symmetry, J. Comput. Graph. Statist. 6 (1997) 435-450.
15. D. Pollard, Convergence of Stochastic Processes, Springer, New York, 1984.
16. J.P. Romano, Bootstrap and randomization tests of some nonparametric hypotheses, Ann. Statist. 17 (1989) 141-159.
17. L.X. Zhu, K.T. Fang, I.M. Bhatti, P.M. Bentler, Testing sphericity of a high-dimensional distribution based on bootstrap approximation, Pakistan J. Statist. 14 (1995) 49-65.
18. L.X. Zhu, G. Neuhaus, Nonparametric Monte Carlo tests for multivariate distribution, Biometrika 67 (2000) 129-153.
19. L.X. Zhu, G. Neuhaus, Conditional test for elliptical symmetry, Technical report, Department of Statistics and Actuarial Science, The University of Hong Kong, 2001.