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Asymptotic distributions of the likelihood ratio test statistics for covariance structures of the complex multivariate normal distributions

Author

Listed:
  • Fang, C.
  • Krishnaiah, P. R.
  • Nagarsenker, B. N.

Abstract

In this paper, the authors derived asymptotic expressions for the null distributions of the likelihood ratio test statistics for multiple independence and multiple homogeneity of the covariance matrices when the underlying distributions are complex multivariate normal. Also, asymptotic expressions are obtained in the non-null cases for the likelihood ratio test statistics for independence of two sets of variables and the equality of two covariance matrices. The expressions obtained in this paper are in terms of beta series. In the null cases, the accuracy of the first terms alone is sufficient for many practical purposes.

Suggested Citation

  • Fang, C. & Krishnaiah, P. R. & Nagarsenker, B. N., 1982. "Asymptotic distributions of the likelihood ratio test statistics for covariance structures of the complex multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 12(4), pages 597-611, December.
    • Handle: RePEc:eee:jmvana:v:12:y:1982:i:4:p:597-611
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    Cited by:

    1. 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.
    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.

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