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Invariant tests for multivariate normality: a critical review

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  • Norbert Henze

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  • Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    • Handle: RePEc:spr:stpapr:v:43:y:2002:i:4:p:467-506
    DOI: 10.1007/s00362-002-0119-6
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    1. Baringhaus, L. & Henze, N., 1991. "Limit distributions for measures of multivariate skewness and kurtosis based on projections," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 51-69, July.
    2. D. R. Cox & Nanny Wermuth, 1994. "Tests of Linearity, Multivariate Normality and the Adequacy of Linear Scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(2), pages 347-355, June.
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    4. N. Henze, 1990. "An approximation to the limit distribution of the epps-pulley test statistic for normality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 37(1), pages 7-18, December.
    5. Gutjahr, Steffen & Henze, Norbert & Folkers, Martin, 1999. "Shortcomings of Generalized Affine Invariant Skewness Measures," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 1-23, October.
    6. J. Koziol, 1987. "An alternative formulation of Neyman’s smooth goodness of fit tests under composite alternatives," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 34(1), pages 17-24, December.
    7. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    8. Sándor Csörgő, 1989. "Consistency of some tests for multivariate normality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 107-116, December.
    9. 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.
    10. Srivastava, M. S., 1984. "A measure of skewness and kurtosis and a graphical method for assessing multivariate normality," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 263-267, October.
    11. Bogdan, Malgorzata, 1999. "Data Driven Smooth Tests for Bivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 26-53, January.
    12. Zhu, Li-Xing & Fang, Kai-Tai & Bhatti, M Ishaq, 1997. "On Estimated Projection Pursuit-Type Crámer-von Mises Statistics, ," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 1-14, October.
    13. Romeu, J. L. & Ozturk, A., 1993. "A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 309-334, August.
    14. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    15. Takafumi Isogai, 1989. "On using influence functions for testing multivariate normality," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(1), pages 169-186, March.
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    17. Norbert Henze, 1997. "Do components of smooth tests of fit have diagnostic properties?," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 121-130, January.
    18. L. Baringhaus & N. Henze, 1988. "A consistent test for multivariate normality based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 339-348, December.
    19. Naito, Kanta, 1998. "Approximation of the Power of Kurtosis Test for Multinormality," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 166-180, May.
    20. 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.
    21. Beirlant, J. & Mason, D. M. & Vynckier, C., 1999. "Goodness-of-fit analysis for multivariate normality based on generalized quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 119-142, April.
    22. Henze, Norbert, 1997. "Extreme smoothing and testing for multivariate normality," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 203-213, October.
    23. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
    24. Epps, T. W., 1999. "Limiting behavior of the ICF test for normality under Gram-Charlier alternatives," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 175-184, April.
    25. Kariya, Takeaki, 1994. "Tests for Multivariate Normality," Economic Review, Hitotsubashi University, vol. 45(2), pages 172-181, April.
    26. Takeaki Kariya & Ruey Tsay & Nobuhiko Terui & Hong Li, 1992. "Tests for Multinormality with Application to Time Series," Discussion Paper Series a264, Institute of Economic Research, Hitotsubashi University.
    27. Bera, A. & John, S., 1983. "Tests for multivariate normality with Pearson alternatives," LIDAM Reprints CORE 534, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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