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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Finner</name><affiliation><mods:affiliation>Universität Trier, Fachbereich IV Mathematik/Statistik D-54286 Trier, Germany</mods:affiliation></affiliation></author><author><name sortKey="Roters, M" sort="Roters, M" uniqKey="Roters M" first="M." last="Roters">M. Roters</name><affiliation><mods:affiliation>Universität Trier, Fachbereich IV Mathematik/Statistik D-54286 Trier, Germany</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Journal of Statistical Planning and Inference</title><title level="j" type="abbrev">JSPI</title><idno type="ISSN">0378-3758</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1999">1999</date><biblScope unit="volume">79</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="11">11</biblScope><biblScope unit="page" to="30">30</biblScope></imprint><idno type="ISSN">0378-3758</idno></series><idno type="istex">4006A197D5118B01013A9FF5F7CFCACB6E5BE985</idno><idno type="DOI">10.1016/S0378-3758(98)00233-X</idno><idno type="PII">S0378-3758(98)00233-X</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0378-3758</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><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></front></TEI><istex><corpusName>elsevier</corpusName><author><json:item><name>H. Finner</name><affiliations><json:string>Universität Trier, Fachbereich IV Mathematik/Statistik D-54286 Trier, Germany</json:string></affiliations></json:item><json:item><name>M. Roters</name><affiliations><json:string>Universität Trier, Fachbereich IV Mathematik/Statistik D-54286 Trier, Germany</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>primary 62J15</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>62F05</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>secondary 62F03</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>60F99</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Asymptotic critical value behaviour</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Bonferroni test procedure</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Familywise error rate</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Hazard rate</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Independent p-values</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Multiple comparisons</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Multiple level</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Multiple test procedure</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Order statistics</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Step-down test</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Step-up test</value></json:item></subject><language><json:string>eng</json:string></language><originalGenre><json:string>Full-length article</json:string></originalGenre><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.</abstract><qualityIndicators><score>7.304</score><pdfVersion>1.2</pdfVersion><pdfPageSize>408 x 660 pts</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>15</keywordCount><abstractCharCount>1314</abstractCharCount><pdfWordCount>7400</pdfWordCount><pdfCharCount>32952</pdfCharCount><pdfPageCount>20</pdfPageCount><abstractWordCount>192</abstractWordCount></qualityIndicators><title>Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures</title><pii><json:string>S0378-3758(98)00233-X</json:string></pii><refBibs><json:item><author><json:item><name>S.R. Dalal</name></json:item><json:item><name>C.L. Mallows</name></json:item></author><host><volume>2</volume><pages><last>765</last><first>752</first></pages><author></author><title>Ann. Appl. Probab.</title></host><title>Buying with exact confidence</title></json:item><json:item><host><author></author></host></json:item><json:item><author><json:item><name>H. Finner</name></json:item><json:item><name>G. Giani</name></json:item></author><host><volume>54</volume><pages><last>227</last><first>201</first></pages><author></author><title>J. Statist. Plann. Inference</title></host><title>Duality between multiple testing and selecting</title></json:item><json:item><host><author></author></host></json:item><json:item><author><json:item><name>H. Finner</name></json:item><json:item><name>M. Roters</name></json:item></author><host><volume>46</volume><pages><last>349</last><first>343</first></pages><author></author><title>Ann. Inst. Statist. Math.</title></host><title>On the limit behaviour of the joint distribution function of order statistics</title></json:item><json:item><author><json:item><name>H. Finner</name></json:item><json:item><name>M. Roters</name></json:item></author><host><volume>26</volume><pages><last>524</last><first>505</first></pages><author></author><title>Ann. Statist.</title></host><title>Asymptotic comparison of step-down and step-up multiple test procedures based on exchangeable test statistics</title></json:item><json:item><host><author></author></host></json:item><json:item><author><json:item><name>Y. Hochberg</name></json:item></author><host><volume>75</volume><pages><last>802</last><first>800</first></pages><author></author><title>Biometrika</title></host><title>A sharper Bonferroni procedure for multiple tests of significance</title></json:item><json:item><author><json:item><name>G. 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Assoc.</title></host><title>Stepwise multiple comparison procedures</title></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>79</volume><pii><json:string>S0378-3758(00)X0076-6</json:string></pii><pages><last>30</last><first>11</first></pages><issn><json:string>0378-3758</json:string></issn><issue>1</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>Journal of Statistical Planning and Inference</title><publicationDate>1999</publicationDate></host><categories><wos><json:string>science</json:string><json:string>statistics & probability</json:string></wos><scienceMetrix><json:string>natural sciences</json:string><json:string>mathematics & statistics</json:string><json:string>statistics & probability</json:string></scienceMetrix></categories><publicationDate>1999</publicationDate><copyrightDate>1999</copyrightDate><doi><json:string>10.1016/S0378-3758(98)00233-X</json:string></doi><id>4006A197D5118B01013A9FF5F7CFCACB6E5BE985</id><score>0.96200603</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/4006A197D5118B01013A9FF5F7CFCACB6E5BE985/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/4006A197D5118B01013A9FF5F7CFCACB6E5BE985/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/4006A197D5118B01013A9FF5F7CFCACB6E5BE985/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>ELSEVIER</publisher><availability><p>ELSEVIER</p></availability><date>1999</date></publicationStmt><notesStmt><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></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures</title><author xml:id="author-1"><persName><forename type="first">H.</forename><surname>Finner</surname></persName><note type="correspondence"><p>Corresponding author</p></note><affiliation>Universität Trier, Fachbereich IV Mathematik/Statistik D-54286 Trier, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">M.</forename><surname>Roters</surname></persName><affiliation>Universität Trier, Fachbereich IV Mathematik/Statistik D-54286 Trier, Germany</affiliation></author></analytic><monogr><title level="j">Journal of Statistical Planning and Inference</title><title level="j" type="abbrev">JSPI</title><idno type="pISSN">0378-3758</idno><idno type="PII">S0378-3758(00)X0076-6</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1999"></date><biblScope unit="volume">79</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="11">11</biblScope><biblScope unit="page" to="30">30</biblScope></imprint></monogr><idno type="istex">4006A197D5118B01013A9FF5F7CFCACB6E5BE985</idno><idno type="DOI">10.1016/S0378-3758(98)00233-X</idno><idno type="PII">S0378-3758(98)00233-X</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1999</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>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.</p></abstract><textClass><keywords scheme="keyword"><list><head>MSC</head><item><term>primary 62J15</term></item><item><term>62F05</term></item><item><term>secondary 62F03</term></item><item><term>60F99</term></item></list></keywords></textClass><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>Asymptotic critical value behaviour</term></item><item><term>Bonferroni test procedure</term></item><item><term>Familywise error rate</term></item><item><term>Hazard rate</term></item><item><term>Independent p-values</term></item><item><term>Multiple comparisons</term></item><item><term>Multiple level</term></item><item><term>Multiple test procedure</term></item><item><term>Order statistics</term></item><item><term>Step-down test</term></item><item><term>Step-up test</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1999">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/4006A197D5118B01013A9FF5F7CFCACB6E5BE985/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: ce:floats; body; tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>JSPI</jid><aid>1481</aid><ce:pii>S0378-3758(98)00233-X</ce:pii><ce:doi>10.1016/S0378-3758(98)00233-X</ce:doi><ce:copyright year="1999" type="unknown"></ce:copyright></item-info><head><ce:title>Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures</ce:title><ce:author-group><ce:author><ce:given-name>H.</ce:given-name><ce:surname>Finner</ce:surname><ce:cross-ref refid="CORR1">*</ce:cross-ref></ce:author><ce:author><ce:given-name>M.</ce:given-name><ce:surname>Roters</ce:surname></ce:author><ce:affiliation id="AFF1"><ce:label>affl1</ce:label><ce:textfn>Universität Trier, Fachbereich IV Mathematik/Statistik D-54286 Trier, Germany</ce:textfn></ce:affiliation><ce:correspondence id="CORR1"><ce:label>*</ce:label><ce:text>Corresponding author</ce:text></ce:correspondence></ce:author-group><ce:date-received day="4" month="11" year="1997"></ce:date-received><ce:date-accepted day="14" month="10" year="1998"></ce:date-accepted><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>We consider the problem of comparing step-down and step-up multiple test procedures for testing <ce:italic>n</ce:italic> hypotheses when independent <ce:italic>p</ce:italic>-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 <ce:italic>p</ce:italic>-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 <ce:italic>n</ce:italic>.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords class="msc"><ce:section-title>MSC</ce:section-title><ce:keyword><ce:text>primary 62J15</ce:text></ce:keyword><ce:keyword><ce:text>62F05</ce:text></ce:keyword><ce:keyword><ce:text>secondary 62F03</ce:text></ce:keyword><ce:keyword><ce:text>60F99</ce:text></ce:keyword></ce:keywords><ce:keywords class="keyword"><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Asymptotic critical value behaviour</ce:text></ce:keyword><ce:keyword><ce:text>Bonferroni test procedure</ce:text></ce:keyword><ce:keyword><ce:text>Familywise error rate</ce:text></ce:keyword><ce:keyword><ce:text>Hazard rate</ce:text></ce:keyword><ce:keyword><ce:text>Independent <ce:italic>p</ce:italic>-values</ce:text></ce:keyword><ce:keyword><ce:text>Multiple comparisons</ce:text></ce:keyword><ce:keyword><ce:text>Multiple level</ce:text></ce:keyword><ce:keyword><ce:text>Multiple test procedure</ce:text></ce:keyword><ce:keyword><ce:text>Order statistics</ce:text></ce:keyword><ce:keyword><ce:text>Step-down test</ce:text></ce:keyword><ce:keyword><ce:text>Step-up test</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Asymptotic comparison of the critical values of step-down and step-up multiple comparison procedures</title></titleInfo><name type="personal"><namePart type="given">H.</namePart><namePart type="family">Finner</namePart><affiliation>Universität Trier, Fachbereich IV Mathematik/Statistik D-54286 Trier, Germany</affiliation><description>Corresponding author</description><role><roleTerm type="text">author</roleTerm></role></name><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><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">1999</dateIssued><copyrightDate encoding="w3cdtf">1999</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><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><recordInfo><recordContentSource>ELSEVIER</recordContentSource></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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