Multivariate Behrens-Fisher problem using means of auxiliary variables

The authors considered the problem of testing equality of two multivariate normal mean vectors when the covariance matrices are unknown and arbitrary. Given auxiliary variables with known means, the authors proposed a pivotal quantity which is similar to the Hotelling T-2 statistic and obtained a satisfying approximation to its distribution. The authors also outlined hypothesis testing and confidence estimation based on the approximate distribution. The merits of the test were studied using Monte Carlo simulation. Monte Carlo studies indicated that the test is very satisfactory even for moderately small samples. At last, the authors illustrated the proposed methods by an example.