On δ-Equivalence With the Best in k-Sample Models

Autor:	K Strassburger, H Finner
Rok vydání:	2006
Předmět:	Statistics and Probability Mathematical optimization Threshold limit value Sample size determination Multiple comparisons problem Projection method Calculus Statistics Probability and Uncertainty Equivalence (measure theory) Statistical hypothesis testing Mathematics
Zdroj:	Journal of the American Statistical Association. 101:737-746
ISSN:	1537-274X 0162-1459
DOI:	10.1198/016214505000001014
Popis:	In recent work we introduced a general, a weak, and a strong partitioning principles for the construction of multiple decision procedures as multiple testing or selection procedures. Partitioning principles can be viewed as natural extensions of the closure principle and sometimes yield more powerful decision procedures. In this article we consider the problem of establishing equivalence with the best with respect to k treatment means, where equivalence is defined in terms of a threshold value δ > 0. We reformulate the original selection problem as a multiple testing problem and develop various step-down and step-up procedures by applying the closure principle and partitioning principles. The new step-down procedure is shown to provide a uniform improvement over procedures currently in use. Moreover, we propose some projection methods that yield confidence intervals being compatible with stepwise tests and selection procedures.
Databáze:	OpenAIRE
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