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On testing for the mean vector of a multivariate distribution with generalized and {2}-inverses


  • Duchesne, Pierre
  • Francq, Christian


Generalized Wald's method constructs testing procedures having chi-squared limiting distributions from test statistics having singular normal limiting distributions by use of generalized inverses. In this article, the use of two-inverses for that problem is investigated, in order to propose new test statistics with convenient asymptotic chi-square distributions. Alternatively, Imhof-based test statistics can also be defined, which converge in distribution to weighted sum of chi-square variables; The critical values of such procedures can be found using Imhof's (1961) algorithm. The asymptotic distributions of the test statistics under the null and alternative hypotheses are discussed. Under fixed and local alternatives, the asymptotic powers are compared theoretically. Simulation studies are also performed to compare the exact powers of the test statistics in finite samples. A data analysis on the temperature and precipitation variability in the European Alps illustrates the proposed methods.

Suggested Citation

  • Duchesne, Pierre & Francq, Christian, 2010. "On testing for the mean vector of a multivariate distribution with generalized and {2}-inverses," MPRA Paper 19740, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:19740

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    References listed on IDEAS

    1. Andrews, Donald W. K., 1987. "Asymptotic Results for Generalized Wald Tests," Econometric Theory, Cambridge University Press, vol. 3(03), pages 348-358, June.
    2. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
    3. Bhimasankaram, P. & Sengupta, D., 1991. "Testing for the mean vector of a multivariate normal distribution with a possibly singular dispersion matrix and related results," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 473-478, June.
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    More about this item


    two-inverses; generalized Wald's method; generalized inverses; multivariate analysis; singular normal distribution;

    JEL classification:

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

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