Complete Classes for Sequential Tests of Hypotheses

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dc.contributor.authorBrown, Lawrence D
dc.contributor.authorCohen, Arthur
dc.contributor.authorStrawderman, William E
dc.date2023-05-17T15:18:09.000
dc.date.accessioned2023-05-23T03:35:08Z
dc.date.available2023-05-23T03:35:08Z
dc.date.issued1980
dc.date.submitted2016-08-05T09:39:41-07:00
dc.description.abstractWe consider problems of sequential testing when the loss function is the sum of a component due to an error in the terminal decision and a cost of observation component. In all cases we establish a characterization of a complete class or an essentially complete class. In order to obtain such results for testing a null hypothesis against an alternative hypothesis we establish complete class results for testing the closure of the null hypothesis against the closure of the alternative hypothesis. A complete class for testing closure of null against closure of alternative is an essentially complete class for testing null against alternative. Furthermore, a complete class for testing closure of null against closure of alternative is a complete class for testing null against alternative when the risks have certain continuity properties. Such continuity properties do hold in many cases. Three models are treated. The first is when the closure of the null space is compact and the cost of the first observation is positive. Under very unrestrictive conditions it is shown that the Bayes tests form a complete class. This result differs considerably from most fixed sample analogues that have been studied. The second model is when the closure of the null space is compact, the distributions are exponential family, and the cost of the first observation is zero. The third model is for the one dimensional exponential family case when the hypotheses are one sided.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/47645
dc.legacy.articleid1324
dc.legacy.fields10.1214/aos/1176344959
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1324&context=statistics_papers&unstamped=1
dc.source.beginpage377
dc.source.endpage398
dc.source.issue277
dc.source.issue2
dc.source.journalStatistics Papers
dc.source.journaltitleThe Annals of Statistics
dc.source.peerreviewedtrue
dc.source.statuspublished
dc.source.volume8
dc.subject.othersequential tests
dc.subject.othercomplete classes
dc.subject.otherBayes tests
dc.subject.othergeneralized Bayes tests
dc.subject.otheradmissibility
dc.subject.otherstopping rules
dc.subject.otherStatistics and Probability
dc.titleComplete Classes for Sequential Tests of Hypotheses
dc.typeArticle
digcom.contributor.authorBrown, Lawrence D
digcom.contributor.authorCohen, Arthur
digcom.contributor.authorStrawderman, William E
digcom.identifierstatistics_papers/277
digcom.identifier.contextkey8933521
digcom.identifier.submissionpathstatistics_papers/277
digcom.typearticle
dspace.entity.typePublication
upenn.schoolDepartmentCenterStatistics Papers
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