The Annals of Statistics

Combining Independent One-Sided Noncentral $t$ or Normal Mean Tests

John I. Marden

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The admissibility of inadmissibility of procedures for combining several one-sided tests of significance into one overall test when the individual tests are based on independent normal or noncentral $t$ variables is considered. Minimal complete classes are found, from which the following results (with some exceptions) are obtained. The likelihood ratio tests and Tippett's procedure are admissible in both cases, the inverse logistic and sum of significance levels procedures are inadmissible in both cases, and Fisher's and the inverse normal procedure are admissible in the normal case but inadmissible in the $t$ case.

Article information

Ann. Statist., Volume 13, Number 4 (1985), 1535-1553.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62C07: Complete class results
Secondary: 62C15: Admissibility 62H15: Hypothesis testing 62C10: Bayesian problems; characterization of Bayes procedures

Hypothesis tests generalized Bayes tests normal variables noncentral $t$ variables admissibility complete class significance levels combination procedures


Marden, John I. Combining Independent One-Sided Noncentral $t$ or Normal Mean Tests. Ann. Statist. 13 (1985), no. 4, 1535--1553. doi:10.1214/aos/1176349754.

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