The Annals of Statistics

On the Inadmissibility of Step-Down Procedures for the Hotelling $T^2$ Problem

John I. Marden and Michael D. Perlman

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Step-down testing procedures for the Hotelling $T^2$ problem are considered. It is shown that the classical step-down procedure proposed by S. N. Roy, R. E. Bargmann and J. Roy is inadmissible among invariant procedures (for a suitable invariance group) in many situations, including all those for which more than two steps are contemplated. It is also noted that in most cases, the power of the step-down procedure decreases in at least one of the noncentrality parameters over part of the parameter space. Finally, several alternative admissible step-down procedures are proposed.

Article information

Ann. Statist., Volume 18, Number 1 (1990), 172-190.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62H15: Hypothesis testing
Secondary: 62C07: Complete class results 62F03: Hypothesis testing

Step-down testing procedures admissibility invariant procedures Hotelling $T^2$ problem minimal complete class


Marden, John I.; Perlman, Michael D. On the Inadmissibility of Step-Down Procedures for the Hotelling $T^2$ Problem. Ann. Statist. 18 (1990), no. 1, 172--190. doi:10.1214/aos/1176347497.

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