The Behrens-Fisher Problem for Regression Coefficients

Abstract

For two normal populations with unknown variances and means depending linearly on $p + q$ regression variables, a Behrens-Fisher generalization is to test the equality of $q$ regression coefficients in one population with a corresponding set in the second population. When $q = 1$ a general class of similar regions is obtained for the hypothesis, and for regions restricted to this class a most powerful or most powerful unbiased test is found. When $q > 1$ several tests are presented and discussed.