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Some new tests for multivariate normality
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  • Published: December 1991

Some new tests for multivariate normality

  • Adolfo J. Quiroz1 &
  • R. M. Dudley2 

Probability Theory and Related Fields volume 87, pages 521–546 (1991)Cite this article

  • 155 Accesses

  • 14 Citations

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Summary

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.

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Author information

Authors and Affiliations

  1. Departamento de Matematicas, Universidad Simon Bolivar, Apartado Postal 80659, 1080-A, Caracas, Venezuela

    Adolfo J. Quiroz

  2. Department of Mathematics, M.I.T., 02139, Cambridge, MA, USA

    R. M. Dudley

Authors
  1. Adolfo J. Quiroz
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  2. R. M. Dudley
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Additional information

The research of this author was carried out in part while at M.I.T. and then at Bell Communications Research

The research of this author was partially supported by National Science Foundation Grants

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Quiroz, A.J., Dudley, R.M. Some new tests for multivariate normality. Probab. Th. Rel. Fields 87, 521–546 (1991). https://doi.org/10.1007/BF01304278

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  • Received: 30 November 1988

  • Revised: 15 June 1990

  • Issue Date: December 1991

  • DOI: https://doi.org/10.1007/BF01304278

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Asymptotic Distribution
  • Parametric Family
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