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LBI tests for multivariate normality in exponential power distributions

Author

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  • Kuwana, Yoichi
  • Kariya, Takeaki

Abstract

In the class of multivariate exponential power distributions, we derive LBI (locally best invariant) tests for normality in the two cases: (i) mean vector [mu] is known and (ii) [mu] is unknown. In the case (i), the null and nonnull asymptotic distributions of the test statistic are derived. In the case (ii) the asymptotic properties of the LBI test remain open because of a technical difficulty. However, the null distribution of a modified test is derived. A Monte Carlo study on the percentage points of the tests is made.

Suggested Citation

  • Kuwana, Yoichi & Kariya, Takeaki, 1991. "LBI tests for multivariate normality in exponential power distributions," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 117-134, October.
    • Handle: RePEc:eee:jmvana:v:39:y:1991:i:1:p:117-134
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    Citations

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    Cited by:

    1. L. Fattorini & C. Pisani, 2000. "Assessing multivariate normality on the "worst" sample configuration," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 23-38.
    2. Saralees Nadarajah, 2006. "Acknowledgement of Priority: the Generalized Normal Distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(9), pages 1031-1032.
    3. Fourdrinier, Dominique & Lemaire, Anne-Sophie, 2002. "Estimation under l1-Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 303-323, November.
    4. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    5. Wolf-Dieter Richter, 2017. "Statistical reasoning in dependent p-generalized elliptically contoured distributions and beyond," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.
    6. Boente, Graciela & Salibián Barrera, Matías & Tyler, David E., 2014. "A characterization of elliptical distributions and some optimality properties of principal components for functional data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 254-264.

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