Two-stage likelihood ratio and union-intersection tests for one-sided alternatives multivariate mean with nuisance dispersion matrix

For a multinormal distribution with an unknown dispersion matrix, union-int ersection (U1) tests for the mean against one-sided alternatives are consid ered. The null distribution of the Ui test statistic is derived and its pow er monotonicity properties are studied. A Stain-type two-stags procedure is proposed to eliminate some of the inherent drawbacks of such tests. Some c omparisons are also made with some recently proposed alternative conditiona l likelihood ratio tests. (C) 1999 Academic Press. AMS 1991 subject classif ications: 62H15, 62L10.