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More on the inadmissibility of step-up

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  • Cohen, Arthur
  • Sackrowitz, Harold B.

Abstract

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).

Suggested Citation

  • Cohen, Arthur & Sackrowitz, Harold B., 2007. "More on the inadmissibility of step-up," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 481-492, March.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:481-492
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Youngjo Lee & Jan F. Bjørnstad, 2013. "Extended likelihood approach to large-scale multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 553-575, June.
    2. Gordon, Alexander Y., 2014. "Smoothing of stepwise multiple testing procedures," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 149-157.
    3. 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.
    4. Michele Guindani & Peter Müller & Song Zhang, 2009. "A Bayesian discovery procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 905-925, November.

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