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Convexity issues in multivariate multiple testing of treatments vs. control

Author

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  • Cohen, Arthur
  • Sackrowitz, Harold

Abstract

The problem of multiple testing of each of several treatment mean vectors versus a control mean vector is considered. Both one-sided and two-sided alternatives are treated. It is shown that typical choices for marginal test procedures will lead to step-down procedures that do not have convex acceptance regions. This lack of convexity has both intuitive and theoretical disadvantages. The only exception being linear tests in the one-sided problem. Although such a procedure is atypical, it not only has convex acceptance regions but is such that critical values are obtainable so that the overall procedure can control FDR or FWER.

Suggested Citation

  • Cohen, Arthur & Sackrowitz, Harold, 2016. "Convexity issues in multivariate multiple testing of treatments vs. control," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 1-11.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:1-11
    DOI: 10.1016/j.jmva.2015.08.010
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