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Simultaneous Confidence Regions Corresponding to Holm's Step-Down Procedure and Other Closed-Testing Procedures
- Source :
- Biometrical Journal. 50:678-692
- Publication Year :
- 2008
- Publisher :
- Wiley, 2008.
-
Abstract
- Holm's (1979) step-down multiple-testing procedure (MTP) is appealing for its flexibility, transparency, and general validity, but the derivation of corresponding simultaneous confidence regions has remained an unsolved problem. This article provides such confidence regions. In fact, simultanenous confidence regions are provided for any MTP in the class of short-cut consonant closed-testing procedures based on marginal p -values and weighted Bonferroni tests for intersection hypotheses considered by Hommel, Bretz and Maurer (2007). In addition to Holm's MTP, this class includes the fixed-sequence MTP, recently proposed gatekeeping MTPs, and the fallback MTP. The simultaneous confidence regions are generally valid if underlying marginal p -values and corresponding marginal confidence regions (assumed to be available) are valid. The marginal confidence regions and estimated quantities are not assumed to be of any particular kinds/dimensions. Compared to the rejections made by the MTP for the family of null hypotheses H under consideration, the proposed confidence regions provide extra free information. In particular, with Holm's MTP, such extra information is provided: for all nonrejected H s, in case not all H s are rejected; or for certain (possibly all) H s, in case all H s are rejected. In case not all H s are rejected, no extra information is provided for rejected H s. This drawback seems however difficult to overcome. Illustrations concerning clinical studies are given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
- Subjects :
- Statistics and Probability
Biometry
Models, Statistical
General Medicine
Confidence interval
symbols.namesake
Closed testing procedure
Bonferroni correction
Statistics
Confidence Intervals
symbols
p-value
Statistics, Probability and Uncertainty
Marginal distribution
Equivalence (measure theory)
Algorithms
Mathematics
Statistical hypothesis testing
Confidence region
Subjects
Details
- ISSN :
- 15214036 and 03233847
- Volume :
- 50
- Database :
- OpenAIRE
- Journal :
- Biometrical Journal
- Accession number :
- edsair.doi.dedup.....93f08e09668c41bbdf1ee2a903e411b2