NEW WEIGHTED SUM OF X(2) TEST FOR TESTING A LINEAR-HYPOTHESIS AGAINST A RESTRICTED ALTERNATIVE HYPOTHESIS

For a statistical test problem against a restricted alternative hypothesis, the author proposes a new weighted sum of the chi(2) test using eigenvectors and eigenvalues of the variance and covariance matrix xi G of mean vector gamma of multivariate random variable Y for the variance and covariance matrix Omega of Y. It is proved that the proposed test is the Bayes test. Powers of the proposed test are compared with those of other tests.