A practical solution to the multivariate Behrens-Fisher problem

Abstract

SUMMARY A practical solution to the multivariate Behrens-Fisher problem is proposed. The new procedure is constructed using the geometry of confidence ellipsoids for the two mean vectors and the condition under which two ellipsoids have no points in common. The new procedure is another extension of the Welch approximate degrees-of-freedom solution as is Yao's (1965) procedure. The new procedure is compared with Yao' s procedure in terms of the level of significance and power using Monte Carlo simulation.