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February 2005 Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure
Arthur Cohen, Harold B. Sackrowitz
Ann. Statist. 33(1): 145-158 (February 2005). DOI: 10.1214/009053604000000986


The problem of multiple endpoint testing for k endpoints is treated as a 2k finite action problem. The loss function chosen is a vector loss function consisting of two components. The two components lead to a vector risk. One component of the vector risk is the false rejection rate (FRR), that is, the expected number of false rejections. The other component is the false acceptance rate (FAR), that is, the expected number of acceptances for which the corresponding null hypothesis is false. This loss function is more stringent than the positive linear combination loss function of Lehmann [Ann. Math. Statist. 28 (1957) 1–25] and Cohen and Sackrowitz [Ann. Statist. (2005) 33 126–144] in the sense that the class of admissible rules is larger for this vector risk formulation than for the linear combination risk function. In other words, fewer procedures are inadmissible for the vector risk formulation. The statistical model assumed is that the vector of variables Z is multivariate normal with mean vector μ and known intraclass covariance matrix Σ. The endpoint hypotheses are Hii=0 vs Kii>0, i=1,…,k. A characterization of all symmetric Bayes procedures and their limits is obtained. The characterization leads to a complete class theorem. The complete class theorem is used to provide a useful necessary condition for admissibility of a procedure. The main result is that the step-up multiple endpoint procedure is shown to be inadmissible.


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Arthur Cohen. Harold B. Sackrowitz. "Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure." Ann. Statist. 33 (1) 145 - 158, February 2005.


Published: February 2005
First available in Project Euclid: 8 April 2005

zbMATH: 1066.62010
MathSciNet: MR2157799
Digital Object Identifier: 10.1214/009053604000000986

Primary: 62C10 , 62C15

Keywords: Bayes procedures , complete class , finite action problem , inadmissibility , intraclass correlation , Schur convexity , step-up procedure

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.33 • No. 1 • February 2005
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