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Invariant tests for symmetry about an unspecified point based on the empirical characteristic function

Author

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  • Henze, N.
  • Klar, B.
  • Meintanis, S. G.

Abstract

This paper considers a flexible class of omnibus affine invariant tests for the hypothesis that a multivariate distribution is symmetric about an unspecified point. The test statistics are weighted integrals involving the imaginary part of the empirical characteristic function of suitably standardized given data, and they have an alternative representation in terms of an L2-distance of nonparametric kernel density estimators. Moreover, there is a connection with two measures of multivariate skewness. The tests are performed via a permutational procedure that conditions on the data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:2:p:275-297
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    References listed on IDEAS

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    1. Neuhaus, Georg & Zhu, Li-Xing, 1998. "Permutation Tests for Reflected Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 129-153, November.
    2. Koziol, James A., 1985. "A note on testing symmetry with estimated parameters," Statistics & Probability Letters, Elsevier, vol. 3(4), pages 227-230, July.
    3. Heathcote, C. R. & Rachev, S. T. & Cheng, B., 1995. "Testing Multivariate Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 91-112, July.
    4. Henze, Norbert, 1997. "Extreme smoothing and testing for multivariate normality," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 203-213, October.
    5. Henze, Norbert & Wagner, Thorsten, 1997. "A New Approach to the BHEP Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 1-23, July.
    6. Koltchinskii, V. I. & Li, Lang, 1998. "Testing for Spherical Symmetry of a Multivariate Distribution," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 228-244, May.
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