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Obtaining the exact and near-exact distributions of the likelihood ratio statistic to test circular symmetry through the use of characteristic functions

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  • Filipe Marques
  • Carlos Coelho

Abstract

In this paper the authors show how through the use of the characteristic function of the negative logarithm of the likelihood ratio test (l.r.t.) statistic to test circular symmetry it is possible to obtain highly manageable expressions for the exact distribution of such statistic, when the number of variables, $$p$$ , is odd, and highly manageable and accurate approximations for an even $$p$$ . For the case of an even $$p$$ , two kinds of near-exact distributions are developed for the l.r.t. statistic which correspond, for the logarithm of the l.r.t. statistic, to a Generalized Near-Integer Gamma distribution or finite mixtures of these distributions. Numerical studies conducted in order to assess the quality of these new approximations show their impressive performance, namely when compared with the only available asymptotic distribution in the literature. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:5:p:2091-2115
    DOI: 10.1007/s00180-013-0398-5
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    References listed on IDEAS

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    1. 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.
    2. Arnold, Barry C. & Coelho, Carlos A. & Marques, Filipe J., 2013. "The distribution of the product of powers of independent uniform random variables — A simple but useful tool to address and better understand the structure of some distributions," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 19-36.
    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.
    4. 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.
    5. Coelho, Carlos A. & Marques, Filipe J., 2010. "Near-exact distributions for the independence and sphericity likelihood ratio test statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 583-593, March.
    6. Nagar, Daya K. & Chen, Jie & Gupta, Arjun K., 2004. "Distribution and percentage points of the likelihood ratio statistic for testing circular symmetry," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 79-89, August.
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    Cited by:

    1. Filipe J. Marques & Carlos A. Coelho & Paulo C. Rodrigues, 2017. "Testing the equality of several linear regression models," Computational Statistics, Springer, vol. 32(4), pages 1453-1480, December.

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