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The multivariate Behrens-Fisher distribution

Author

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  • Girón, Fco. Javier
  • del Castillo, Carmen

Abstract

The main purpose of this paper is the study of the multivariate Behrens-Fisher distribution. It is defined as the convolution of two independent multivariate Student t distributions. Some representations of this distribution as the mixture of known distributions are shown. An important result presented in the paper is the elliptical condition of this distribution in the special case of proportional scale matrices of the Student t distributions in the defining convolution. For the bivariate Behrens-Fisher problem, the authors propose a non-informative prior distribution leading to highest posterior density (H.P.D.) regions for the difference of the mean vectors whose coverage probability matches the frequentist coverage probability more accurately than that obtained using the independence-Jeffreys prior distribution, even with small samples.

Suggested Citation

  • Girón, Fco. Javier & del Castillo, Carmen, 2010. "The multivariate Behrens-Fisher distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2091-2102, October.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:2091-2102
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    References listed on IDEAS

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    1. D. Nel & P. Groenewald, 1993. "A Bayesian approach to the multivariate Behrens-Fisher problem under the assumption of proportional covariance matrices," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(1), pages 111-124, December.
    2. Gamage, Jinadasa & Mathew, Thomas & Weerahandi, Samaradasa, 2004. "Generalized p-values and generalized confidence regions for the multivariate Behrens-Fisher problem and MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 177-189, January.
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    Cited by:

    1. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.

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