The multivariate Behrens-Fisher distribution

Fco. Javier Girón and Carmen del Castillo

Journal of Multivariate Analysis, 2010, vol. 101, issue 9, 2091-2102

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.

Keywords: Multivariate; Behrens-Fisher; distribution; Convolution; Mixture; H.P.D.; regions; Monte; Carlo; methods; Frequentist; coverage (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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