Testing for Spherical Symmetry of a Multivariate Distribution
AbstractWe consider a test for spherical symmetry of a distribution in dwith an unknown center. It is a multivariate version of the tests suggested by Schuster and Barker and by Arcones and Giné. The test statistic is based on the multivariate extension of the distribution and quantile functions, recently introduced by Koltchinskii and Dudley and by Chaudhuri. We study the asymptotic behavior of the sequence of test statistics for large samples and for a fixed spherically asymmetric alternative as well as for a sequence of local alternatives converging to a spherically symmetric distribution. We also study numerically the performance of the test for moderate sample sizes and justify a symmetrized version of bootstrap approximation of the distribution of test statistics.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 65 (1998)
Issue (Month): 2 (May)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Einmahl, J.H.J. & Gantner, M., 2010. "Testing for Bivariate Spherical Symmetry," Discussion Paper 2010-71, Tilburg University, Center for Economic Research.
- Sakhanenko, Lyudmila, 2008. "Testing for ellipsoidal symmetry: A comparison study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 565-581, December.
- Jiajuan Liang & Kai-Tai Fang & Fred Hickernell, 2008. "Some necessary uniform tests for spherical symmetry," Annals of the Institute of Statistical Mathematics, Springer, vol. 60(3), pages 679-696, September.
- Henze, N. & Klar, B. & Meintanis, S. G., 2003. "Invariant tests for symmetry about an unspecified point based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 275-297, November.
- Manzotti, A. & Pérez, Francisco J. & Quiroz, Adolfo J., 2002. "A Statistic for Testing the Null Hypothesis of Elliptical Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 274-285, May.
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