Testing for Spherical Symmetry of a Multivariate Distribution

Journal of Multivariate Analysis

Volumn 65, Issue 2, 1998, Pages 228-244

  Koltchinskii, V I ^a   Li, Lang ^a  

^a NONE

Author keywords

Empirical processes; Measure of asymmetry of probability distribution; Spherical symmetry; Symmetrized bootstrap; VC subgraph classes

Indexed keywords

EID: 0002397525     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1998.1743     Document Type: Article

References (24)

1. n. Ann. Inst. Statist. Math. 45:1993;787-800.
2. Arcones M., Giné E. Some bootstrap tests of symmetry for univariate continuous distributions. Ann. Statist. 19:1991;1496-1511.
3. Baringhaus L. Testing for spherical symmetry of a multivariate distribution. Ann. Statist. 19:1991;899-917.
4. Bedall F. K., Zimmermann H. Algorithm AS143. The mediancentre. Appl. Statist. 28:1979;325-328.
5. Beran R. Testing for ellipsoidal symmetry of a multivariate density. Ann. Statist. 7:1979;150-162.
6. Beran R., Millar P. W. Confidence sets for a multivariate distribution. Ann. Statist. 14:1986;431-443.
7. Billingsley P., Topsøe F. Uniformity in weak convergence. Z. Wahrsch. verw. Gebiete. 7:1967;1-16.
8. Blough D. K. Multivariate symmetry via projection pursuit. Ann. Inst. Statist. Math. 41:1989;461-475.
9. Chaudhuri P. On a geometric notion of quantiles for multivariate data. J. Amer. Statist. Assoc. 91:1996;862-872.
10. Cirel'son B. S. The density of the distribution of the maximum of a Gaussian process. Theory Probab. Appl. 20:1975;847-855.
11. Csörgö S., Heathcote C. R. Testing for symmetry. Biometrika. 74:1987;177-186.
12. Ghosh S., Ruymgaart F. H. Applications of empirical characteristic functions in some multivariate problems. Canad. J. Statist. 20:1992;429-440.
13. Giné E., Zinn J. Bootstrapping general empirical measures. Ann. Probab. 18:1990;851-869.
14. Giné E., Zinn J. Gaussian characterization of uniform Donsker classes. Ann. Probab. 19:1991;758-782.
15. Gower J. C. Algorithm AS78. The mediancentre. Appl. Statist. 23:1974;466-470.
16. Heathcote C. R., Rachev S. T., Cheng B. Testing multivariate symmetry. J. Multivariate Anal. 54:1995;91-112.
17. Kariya T., Eaton M. L. Robust tests for spherical symmetry. Ann. Statist. 5:1977;206-215.
18. Koltchinskii V. Bahadur-Kiefer approximation for spatial quantiles. Probability in Banach Spaces. 1994a;Birkhäuser, Boston, Cambridge. p. 394-408.
19. Koltchinskii V. Nonlinear transformations of empirical processes: functional inverses and Bahadur-Kiefer representations. Grigelionis B., Kubilius J. Probability Theory and Mathematical Statistics. Proc. of the 5th International Vilnius Conference. 1994b;423-445 VSP-TEV.
20. Koltchinskii V. M. Ann. Statist. 25:1997;435-477.
21. Romano J. P. Bootstrap and randomization tests of some nonparametric hypothesis. Ann. Statist. 17:1989;141-159.
22. Schuster E. F., Barker R. C. Using the bootstrap in testing symmetry versus asymmetry. Comm. Statist. Simulation Comput. 16:1987;69-84.
23. Shorack G. R., Wellner J. A. Empirical Processes with Applications to Statistics. 1986;Wiley, New York.
24. van der Vaart A. W., Wellner J. A. Weak Convergence and Empirical Processes with Applications to Statistics. 1986;Springer-Verlag, Berlin/New York.