Probability Theory and Related Fields

, Volume 87, Issue 4, pp 521–546 | Cite as

Some new tests for multivariate normality

  • Adolfo J. Quiroz
  • R. M. Dudley


A family of statistics is presented that can be used for testing goodness of fit to a parametric family. These statistics include Mardia's measure of multivariate kurtosis and Moore and Stubblebine's test for multivariate normality. The asymptotic distribution of the statistics is found under mild hypotheses on the parametric family and, in the case of multivariate normality, the distribution is shown to be independent of the “true” parameter. A class of tests for multivariate normality is presented and the performance of two such tests in the bivariate case is found in simulations.


Stochastic Process Probability Theory Mathematical Biology Asymptotic Distribution Parametric Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Adolfo J. Quiroz
    • 1
  • R. M. Dudley
    • 2
  1. 1.Departamento de MatematicasUniversidad Simon BolivarCaracasVenezuela
  2. 2.Department of MathematicsM.I.T.CambridgeUSA

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