Generalized p-values and the multivariate Behrens-Fisher problem

Tsui and Weerahandi (1989) defined generalized p-values for testing statistical hypothesis in the presence of nuisance parameters and applied to obtain an exact solution to the univariate Behrens-Fisher problem. Johnson and Weerahandi (1988) provided a Bayesian solution to the multivariate Behrens-Fisher problem. With the help of the Cauchy-Schwarz inequality we provide an upper bound for the generalized p-value for the multivariate case. Also we extend the result of Tsui and Weerahandi to present a second upper bound. (C) Elsevier Science Inc., 1997.