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Testing the hypothesis of a doubly exchangeable covariance matrix for elliptically contoured distributions

Author

Listed:
  • Carlos A. Coelho
  • Anuradha Roy

    (UTSA)

Abstract

In this paper the authors study the problem of testing the hypothesis of a doubly exchangeable covariance matrix for three-level multivariate observations, taken on m variables over u sites and over v time/spatial points. Through the decomposition of the main hypothesis into a set of three sub-hypotheses, the likelihood ratio test statistic is dened, its exact moments determined, and its exact distribution studied. Because this distribution is very much intricate, a very precise near-exact distribution is developed. Numerical studies conducted to evaluate the closeness between this near-exact distribution and the exact distribution show the very good performance of this approximation even for very small sample sizes. A simulation study is also conducted and a real data example is presented..

Suggested Citation

  • Carlos A. Coelho & Anuradha Roy, 2014. "Testing the hypothesis of a doubly exchangeable covariance matrix for elliptically contoured distributions," Working Papers 0145mss, College of Business, University of Texas at San Antonio.
    • Handle: RePEc:tsa:wpaper:0145mss
    as

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    File URL: http://interim.business.utsa.edu/wps/mss/0002MSS-253-2014.pdf
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    References listed on IDEAS

    as
    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. Leiva, Ricardo & Roy, Anuradha, 2012. "Linear discrimination for three-level multivariate data with a separable additive mean vector and a doubly exchangeable covariance structure," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1644-1661.
    3. Filipe Marques & Carlos Coelho & Barry Arnold, 2011. "A general near-exact distribution theory for the most common likelihood ratio test statistics used in Multivariate Analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 180-203, May.
    4. Roy, Anuradha & Leiva, Ricardo, 2008. "Likelihood ratio tests for triply multivariate data with structured correlation on spatial repeated measurements," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1971-1980, September.
    5. 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.
    6. Carlos A. Coelho & Anuradha Roy, 2013. "Testing of hypothesis of a block compound symmetric covariance matrix," Working Papers 0179mss, College of Business, University of Texas at San Antonio.
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    Cited by:

    1. Arkadiusz Koziol & Anuradha Roy & Roman Zmyslony & Ricardo Leiva & Miguel Fonseca, 2016. "Best unbiased estimates for parameters of three-level multivariate data with doubly exchangeable covariance structure," Working Papers 0149mss, College of Business, University of Texas at San Antonio.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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