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Data Driven Smooth Tests for Bivariate Normality

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  • Bogdan, Malgorzata

Abstract

Based upon the idea of construction of data driven smooth tests for composite hypotheses presented in Inglotet al.(1997) and Kallenberg and Ledwina (1997), two versions of data driven smooth test for bivariate normality are proposed. Asymptotic null distributions are derived, and consistency of the newly introduced tests against every bivariate alternative with marginals having finite variances is proved. Included results of power simulations show that one of the proposed tests performs very well in comparison with other commonly used tests for bivariate normality.

Suggested Citation

  • Bogdan, Malgorzata, 1999. "Data Driven Smooth Tests for Bivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 26-53, January.
    • Handle: RePEc:eee:jmvana:v:68:y:1999:i:1:p:26-53
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    References listed on IDEAS

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    1. 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.
    2. N. J. H. Small, 1980. "Marginal Skewness and Kurtosis in Testing Multivariate Normality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 85-87, March.
    3. 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.
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    Cited by:

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    2. Vexler, Albert, 2020. "Univariate likelihood projections and characterizations of the multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    3. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    4. Alessandro Manzotti & Adolfo Quiroz, 2001. "Spherical harmonics in quadratic forms for testing multivariate normality," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 87-104, June.

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