Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures
Identifieur interne : 001750 ( Istex/Corpus ); précédent : 001749; suivant : 001751Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures
Auteurs : H. Finner ; M. RotersSource :
- Journal of Statistical Planning and Inference [ 0378-3758 ] ; 1999.
Abstract
We consider the problem of comparing step-down and step-up multiple test procedures for testing n hypotheses when independent p-values or independent test statistics are available. The defining critical values of these procedures for independent test statistics are asymptotically equal, which yields a theoretical argument for the numerical observation that the step-up procedure is mostly more powerful than the step-down procedure. The main aim of this paper is to quantify the differences between the critical values more precisely. As a by-product we also obtain more information about the gain when we consider two subsequent steps of these procedures. Moreover, we investigate how liberal the step-up procedure becomes when the step-up critical values are replaced by their step-down counterparts or by more refined approximate values. The results for independent p-values are the basis for obtaining corresponding results when independent real-valued test statistics are at hand. It turns out that the differences of step-down and step-up critical values as well as the differences between subsequent steps tend to zero for many distributions, except for heavy-tailed distributions. The Cauchy distribution yields an example where the critical values of both procedures are nearly linearly increasing in n.
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DOI: 10.1016/S0378-3758(98)00233-X
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<front><div type="abstract" xml:lang="en">We consider the problem of comparing step-down and step-up multiple test procedures for testing n hypotheses when independent p-values or independent test statistics are available. The defining critical values of these procedures for independent test statistics are asymptotically equal, which yields a theoretical argument for the numerical observation that the step-up procedure is mostly more powerful than the step-down procedure. The main aim of this paper is to quantify the differences between the critical values more precisely. As a by-product we also obtain more information about the gain when we consider two subsequent steps of these procedures. Moreover, we investigate how liberal the step-up procedure becomes when the step-up critical values are replaced by their step-down counterparts or by more refined approximate values. The results for independent p-values are the basis for obtaining corresponding results when independent real-valued test statistics are at hand. It turns out that the differences of step-down and step-up critical values as well as the differences between subsequent steps tend to zero for many distributions, except for heavy-tailed distributions. The Cauchy distribution yields an example where the critical values of both procedures are nearly linearly increasing in n.</div>
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<notesStmt><note type="content">Table 1: Actual probabilities of accepting all n hypotheses for two approximate step-up procedures</note>
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<affiliation>Universität Trier, Fachbereich IV Mathematik/Statistik D-54286 Trier, Germany</affiliation>
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<name type="personal"><namePart type="given">M.</namePart>
<namePart type="family">Roters</namePart>
<affiliation>Universität Trier, Fachbereich IV Mathematik/Statistik D-54286 Trier, Germany</affiliation>
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<originInfo><publisher>ELSEVIER</publisher>
<dateIssued encoding="w3cdtf">1999</dateIssued>
<copyrightDate encoding="w3cdtf">1999</copyrightDate>
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<abstract lang="en">We consider the problem of comparing step-down and step-up multiple test procedures for testing n hypotheses when independent p-values or independent test statistics are available. The defining critical values of these procedures for independent test statistics are asymptotically equal, which yields a theoretical argument for the numerical observation that the step-up procedure is mostly more powerful than the step-down procedure. The main aim of this paper is to quantify the differences between the critical values more precisely. As a by-product we also obtain more information about the gain when we consider two subsequent steps of these procedures. Moreover, we investigate how liberal the step-up procedure becomes when the step-up critical values are replaced by their step-down counterparts or by more refined approximate values. The results for independent p-values are the basis for obtaining corresponding results when independent real-valued test statistics are at hand. It turns out that the differences of step-down and step-up critical values as well as the differences between subsequent steps tend to zero for many distributions, except for heavy-tailed distributions. The Cauchy distribution yields an example where the critical values of both procedures are nearly linearly increasing in n.</abstract>
<note type="content">Table 1: Actual probabilities of accepting all n hypotheses for two approximate step-up procedures</note>
<note type="content">Table 2: Critical value behaviour of the Cauchy distribution (α=0.05)</note>
<subject><genre>MSC</genre>
<topic>primary 62J15</topic>
<topic>62F05</topic>
<topic>secondary 62F03</topic>
<topic>60F99</topic>
</subject>
<subject><genre>Keywords</genre>
<topic>Asymptotic critical value behaviour</topic>
<topic>Bonferroni test procedure</topic>
<topic>Familywise error rate</topic>
<topic>Hazard rate</topic>
<topic>Independent p-values</topic>
<topic>Multiple comparisons</topic>
<topic>Multiple level</topic>
<topic>Multiple test procedure</topic>
<topic>Order statistics</topic>
<topic>Step-down test</topic>
<topic>Step-up test</topic>
</subject>
<relatedItem type="host"><titleInfo><title>Journal of Statistical Planning and Inference</title>
</titleInfo>
<titleInfo type="abbreviated"><title>JSPI</title>
</titleInfo>
<genre type="journal">journal</genre>
<originInfo><dateIssued encoding="w3cdtf">199906</dateIssued>
</originInfo>
<identifier type="ISSN">0378-3758</identifier>
<identifier type="PII">S0378-3758(00)X0076-6</identifier>
<part><date>199906</date>
<detail type="volume"><number>79</number>
<caption>vol.</caption>
</detail>
<detail type="issue"><number>1</number>
<caption>no.</caption>
</detail>
<extent unit="issue pages"><start>1</start>
<end>178</end>
</extent>
<extent unit="pages"><start>11</start>
<end>30</end>
</extent>
</part>
</relatedItem>
<identifier type="istex">4006A197D5118B01013A9FF5F7CFCACB6E5BE985</identifier>
<identifier type="DOI">10.1016/S0378-3758(98)00233-X</identifier>
<identifier type="PII">S0378-3758(98)00233-X</identifier>
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