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Near-exact distributions for the likelihood ratio test statistic to test equality of several variance-covariance matrices in elliptically contoured distributions


  • Carlos Coelho


  • Filipe Marques



The exact distribution of the likelihood ratio test statistic to test the equality of several variance-covariance matrices has a non-manageable form. On the other hand, the existing asymptotic approximations do not exhibit the necessary precision for many applications. For these reasons, the development of near-exact approximations to the distribution of this statistic, arising from a different method of approximating distributions, emerges as a desirable goal. These distributions, while being manageable are much closer to the exact distribution than the usual asymptotic distributions and opposite to these, are also asymptotic for increasing number of variables and matrices involved. Computational modules to implement the near-exact distributions are made available on a web-site. Copyright Springer-Verlag 2012

Suggested Citation

  • Carlos Coelho & Filipe Marques, 2012. "Near-exact distributions for the likelihood ratio test statistic to test equality of several variance-covariance matrices in elliptically contoured distributions," Computational Statistics, Springer, vol. 27(4), pages 627-659, December.
  • Handle: RePEc:spr:compst:v:27:y:2012:i:4:p:627-659
    DOI: 10.1007/s00180-011-0281-1

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    References listed on IDEAS

    1. Jamshidian, Mortaza & Schott, James R., 2007. "Testing equality of covariance matrices when data are incomplete," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4227-4239, May.
    2. Coelho, Carlos A., 1998. "The Generalized Integer Gamma Distribution--A Basis for Distributions in Multivariate Statistics," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 86-102, January.
    3. Coelho, Carlos A., 2004. "The generalized near-integer Gamma distribution: a basis for 'near-exact' approximations to the distribution of statistics which are the product of an odd number of independent Beta random variables," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 191-218, May.
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    Cited by:

    1. Filipe Marques & Carlos Coelho, 2013. "Obtaining the exact and near-exact distributions of the likelihood ratio statistic to test circular symmetry through the use of characteristic functions," Computational Statistics, Springer, vol. 28(5), pages 2091-2115, October.
    2. repec:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0512-4 is not listed on IDEAS
    3. Carlos Coelho & Barry Arnold & Filipe Marques, 2015. "The exact and near-exact distributions of the main likelihood ratio test statistics used in the complex multivariate normal setting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 386-416, June.


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