Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/79597
Authors: 
Dickhaus, Thorsten
Stange, Jens
Year of Publication: 
2012
Series/Report no.: 
SFB 649 Discussion Paper 2012-041
Abstract: 
We consider a special class of multiple testing problems, consisting of M simultaneous point hypothesis tests in local statistical experiments. Under certain structural assumptions the global hypothesis contains exactly one element v* (say), and v* is least favourable parameter configuration with respect to the family-wise error rate (FWER) of multiple single-step tests, meaning that the FWER of such tests becomes largest under v*. Furthermore, it turns out that concepts of positive dependence are applicable to the involved test statistics in many practically relevant cases, in particular, for multivariate normal and chi-squared distributions. Altogether, this allows for a relaxation of the adjustment for multiplicity by making use of the intrinsic correlation structure in the data. We represent product-type bounds for the FWER in terms of a relaxed éSidák-type correction of the overall significance level and compute effective numbers of tests. Our methodology can be applied to a variety of simultaneous location parameter problems, as in analysis of variance models or in the context of simultaneous categorical data analysis. For example, simultaneous chisquare tests for association of categorical features are ubiquitous in genomewide association studies. In this type of model, Moskvina and Schmidt (2008) gave a formula for an effective number of tests utilizing Pearson's haplotypic correlation coefficient as a linkage disequilibrium measure. Their result follows as a corollary from our general theory and will be generalized.
Subjects: 
Monotonically sub-Markovian
multiple test
multiplicity correction
multivariate chi-squared distribution
positive orthant dependence
Sidák correction
single-step test
subset pivotality
JEL: 
C12
C44
Document Type: 
Working Paper

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