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Testing for Spherical Symmetry of a Multivariate Distribution

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  • Koltchinskii, V. I.
  • Li, Lang
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    Abstract

    We 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 Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 65 (1998)
    Issue (Month): 2 (May)
    Pages: 228-244

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    Handle: RePEc:eee:jmvana:v:65:y:1998:i:2:p:228-244

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    Related research

    Keywords: empirical processes; measure of asymmetry of probability distribution; spherical symmetry; symmetrized bootstrap; VC-subgraph classes;

    References

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    1. Heathcote, C. R. & Rachev, S. T. & Cheng, B., 1995. "Testing Multivariate Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 91-112, July.
    2. David Blough, 1989. "Multivariate symmetry via projection pursuit," Annals of the Institute of Statistical Mathematics, Springer, vol. 41(3), pages 461-475, September.
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    Cited by:
    1. John Einmahl & Maria Gantner, 2012. "Testing for bivariate spherical symmetry," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(1), pages 54-73, March.
    2. 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.
    3. 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.
    4. Sakhanenko, Lyudmila, 2008. "Testing for ellipsoidal symmetry: A comparison study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 565-581, December.

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