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Testing of hypothesis of a block compound symmetric covariance matrix

Author

Listed:
  • Carlos A. Coelho
  • Anuradha Roy

    (UTSA)

Abstract

In this paper the authors study the problem of testing the hypothesis of a block compound symmetry covariance matrix with two-level multivariate observations, taken for m variables over u sites or time points. Through the decomposition of the main hypothesis into two sub-hypotheses, the likelihood ratio test statistic is easily obtained as well as its exact moments. Its exact distribution is then analyzed. Because this distribution is quite elaborate, yielding a non-manageable distribution function, a manageable but 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 real data example is studied and a simulation is also conducted.

Suggested Citation

  • 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.
    • Handle: RePEc:tsa:wpaper:0179mss
    as

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    File URL: http://interim.business.utsa.edu/wps/mss/0012MSS-253-2013.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. 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. 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. 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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    Citations

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    Cited by:

    1. Amitrajeet A. Batabyal & Hamid Beladi, 2015. "Optimal Transport Provision To A Tourist Destination: A Mechanism Design Approach," Working Papers 0140eco, College of Business, University of Texas at San Antonio.
    2. 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.

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    More about this item

    Keywords

    characteristic function; composition of hypothesis; distribution of likelihood ratio statistics; near-exact distributions; product of independent Beta random variables; sum of independent Gamma random variables.;
    All these keywords.

    JEL classification:

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

    Statistics

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