Multivariate multistage methodologies for simultaneous all pairwise comparisons
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We consider the problem of constructing simultaneous fixed-width confidence intervals for all pairwise treatment differences μ1−μ J , in the presence ofk(≥2) independent populationsN p (μ1,Σ), 1≤i≠j≤k. Appropriate purely sequential, accelerated sequential and three-stage sampling strategies have been developed and variousfirst-order asymptotic properties are then derived when Σ pxp is completely unknown, but positive definite (p.d.). In the two special cases when the largest component variance in Σ is a known multiple of one of the variances or Σ=σ2 H where σ(>0) is unknown, butH pxp is known and p.d., the original multistage sampling strategies are specialized. Under such special circumstances, associatedsecond-order characteristics are then developed. It is to be noted that our present formulation and the methodologies fill important voids in the context of multivariate multiple comparisons which is a challenging area that has not yet been fully explored. Moderate sample performances of the proposed techniques were very encouraging and detailed remarks on these were included in Mukhopadhyay and Aoshima (1997).
Key Words and PhrasesMultivariate normal fixed-width second-order analysis sequential procedure accelerated sequential procedure three-stage procedure
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