Step-down testing procedures for the Hotelling T2 problem are considered. We show that the step-down procedure proposed by S.N. Roy, R.E. Bargmann, and J. Roy is inadmissibleamonginvariantprocedures (for a suitable invariance group) in many situatiqns, includiItgallthosefor which more than two steps are contemplated. We also show that in most cases, the power of the step-down procedure decrease...
