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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

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  • Carlos Coelho

    ()

  • Filipe Marques

    ()

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    Abstract

    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

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    File URL: http://hdl.handle.net/10.1007/s00180-011-0281-1
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    Bibliographic Info

    Article provided by Springer in its journal Computational Statistics.

    Volume (Year): 27 (2012)
    Issue (Month): 4 (December)
    Pages: 627-659

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    Handle: RePEc:spr:compst:v:27:y:2012:i:4:p:627-659

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    Related research

    Keywords: Asymptotic approximations; Sum of gamma distributions; Product of beta distributions; Generalized near-integer gamma distribution; Mixtures;

    References

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    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., 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.
    3. 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.
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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.

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