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More on the inadmissibility of step-up


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  • Cohen, Arthur
  • Sackrowitz, Harold B.
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    Cohen and Sackrowitz [Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure, Ann. Statist. 33 (2005) 145-158] proved that the step-up multiple testing procedure is inadmissible for a multivariate normal model with unknown mean vector and known intraclass covariance matrix. The hypotheses tested are each mean is zero vs. each mean is positive. The risk function is a 2x1 vector where one component is average size and the other component is one minus average power. In this paper, we extend the inadmissibility result to several different models, to two-sided alternatives, and to other risk functions. The models include one-parameter exponential families, independent t-variables, independent [chi]2-variables, t-tests arising from the analysis of variance, and t-tests arising from testing treatments against a control. The additional risk functions are linear combinations where one component is the false discovery rate (FDR).

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 3 (March)
    Pages: 481-492

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:481-492

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    Keywords: Multiple testing procedures False discovery rate (FDR) False acceptance rate Classification risk Vector risk Finite action problem Schur convexity;


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    1. Peter Muller & Giovanni Parmigiani & Christian Robert & Judith Rousseau, 2004. "Optimal Sample Size for Multiple Testing: The Case of Gene Expression Microarrays," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 990-1001, December.
    2. Ishwaran H. & Rao J.S., 2003. "Detecting Differentially Expressed Genes in Microarrays Using Bayesian Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 438-455, January.
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    Cited by:
    1. Gordon, Alexander Y., 2014. "Smoothing of stepwise multiple testing procedures," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 149-157.
    2. Ebrahimi, Nader, 2008. "Simultaneous control of false positives and false negatives in multiple hypotheses testing," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 437-450, March.


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