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2012-06-26Diskussionspapier DOI: 10.18452/4414
Multiple point hypothesis test problems and effective numbers of tests
dc.contributor.authorDickhaus, Thorsten
dc.contributor.authorStange, Jens
dc.date.accessioned2017-06-16T00:41:18Z
dc.date.available2017-06-16T00:41:18Z
dc.date.created2012-08-20
dc.date.issued2012-06-26
dc.date.submitted2012-06-26
dc.identifier.issn1860-5664
dc.identifier.urihttp://edoc.hu-berlin.de/18452/5066
dc.description.abstractWe 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 vartheta* (say), and vartheta* 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 vartheta*. 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 Sidak-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.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectmultiple testeng
dc.subjectmultivariate chi-squared distributioneng
dc.subjectMonotonically sub-Markovianeng
dc.subjectmultiplicity correctioneng
dc.subjectpositive orthant dependenceeng
dc.subjectSidák correctioneng
dc.subjectsingle-step testeng
dc.subjectsubset pivotalityeng
dc.subject.ddc330 Wirtschaft
dc.titleMultiple point hypothesis test problems and effective numbers of tests
dc.typeworkingPaper
dc.identifier.urnurn:nbn:de:kobv:11-100203831
dc.identifier.doihttp://dx.doi.org/10.18452/4414
local.edoc.pages22
local.edoc.type-nameDiskussionspapier
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-year2012
dc.identifier.zdb2195055-6
bua.series.nameSonderforschungsbereich 649: Ökonomisches Risiko
bua.series.issuenumber2012,41

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