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A Necessary Test of Goodness of Fit for Sphericity

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  • Fang, K. T.
  • Zhu, L. X.
  • Bentler, P. M.

Abstract

A p - 1 random vector x is said to have a spherical distribution, if for every p - p orthogonal matrix Q, x and Qx have the same distribution. In this paper, some nonparametric goodness of fit Wilcoxon-type tests for sphericity are proposed. Some results on the limiting distributions of the statistics are obtained. These results provide a theoretical basis for a necessary test of sphericity.

Suggested Citation

  • Fang, K. T. & Zhu, L. X. & Bentler, P. M., 1993. "A Necessary Test of Goodness of Fit for Sphericity," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 34-55, April.
    • Handle: RePEc:eee:jmvana:v:45:y:1993:i:1:p:34-55
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    Cited by:

    1. Iwashita, Toshiya & Klar, Bernhard & Amagai, Moe & Hashiguchi, Hiroki, 2017. "A test procedure for uniformity on the Stiefel manifold based on projection," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 89-96.
    2. Batsidis, Apostolos & Zografos, Konstantinos, 2013. "A necessary test of fit of specific elliptical distributions based on an estimator of Song’s measure," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 91-105.
    3. 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.
    4. Neuhaus, Georg & Zhu, Li-Xing, 1998. "Permutation Tests for Reflected Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 129-153, November.
    5. Albisetti, Isaia & Balabdaoui, Fadoua & Holzmann, Hajo, 2020. "Testing for spherical and elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    6. Zhu, Li-Xing & Neuhaus, Georg, 2003. "Conditional tests for elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 284-298, February.
    7. Huiwen Wang & Qiang Liu, 1998. "Forecast modelling for rotations of principal axes of multidimensional data sets," Computational Statistics & Data Analysis, Elsevier, vol. 27(3), pages 345-354, May.
    8. Yuan, Ke-Hai & Bentler, Peter M., 2000. "Inferences on Correlation Coefficients in Some Classes of Nonnormal Distributions," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 230-248, February.

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