On a ranking problem for symmetric and unimodal location parameter families
Identifieur interne : 000457 ( Istex/Corpus ); précédent : 000456; suivant : 000458On a ranking problem for symmetric and unimodal location parameter families
Auteurs : M. RotersSource :
- Statistics and Probability Letters [ 0167-7152 ] ; 1993.
Abstract
Consider a location family of distributions generated by a symmetric and unimodal density w.r.t. Lebesgue measure. In this paper we prove that the probability of correctly ranking k = 3 populations from the above class of distributions subject to the condition that the range of the location parameters is bounded by 2δ is maximized for the parameter configuration (0, δ, 2δ). The corresponding conjecture that for k ⩾ 4 this maximum is also attained for the ‘equally spaced means configuration’ as above has, in general, a negative answer. A counterexample is given for k = 4 in the normal case.
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DOI: 10.1016/0167-7152(93)90121-X
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Eaton</name></json:item></author><host><author></author><title>Lectures on Topics in Probability Inequalities</title></host><title>Lectures on Topics in Probability Inequalities</title></json:item><json:item><host><author></author><title>Inequalities: Theory of Majorization and its Applications</title></host></json:item><json:item><author><json:item><name>I. Olkin</name></json:item><json:item><name>M. Sobel</name></json:item><json:item><name>Y.L. Tong</name></json:item></author><host><volume>2</volume><pages><last>212</last><first>193</first></pages><author></author><title>Statistical Decision Theory and Related Topics III</title></host><title>Bounds for a k-fold integral for location and scale parameter models with applications to statistical ranking and selection problems</title></json:item><json:item><host><author></author><title>The Multivariate Normal Distribution</title></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>16</volume><pii><json:string>S0167-7152(00)X0172-1</json:string></pii><pages><last>49</last><first>47</first></pages><issn><json:string>0167-7152</json:string></issn><issue>1</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>Statistics and Probability Letters</title><publicationDate>1993</publicationDate></host><publicationDate>1993</publicationDate><copyrightDate>1993</copyrightDate><doi><json:string>10.1016/0167-7152(93)90121-X</json:string></doi><id>D61DC1EC421D23A29C5FB3A3D1659BFB36BB956B</id><score>2.4721305</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/D61DC1EC421D23A29C5FB3A3D1659BFB36BB956B/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/D61DC1EC421D23A29C5FB3A3D1659BFB36BB956B/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/D61DC1EC421D23A29C5FB3A3D1659BFB36BB956B/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">On a ranking problem for symmetric and unimodal location parameter families</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>ELSEVIER</publisher><availability><p>ELSEVIER</p></availability><date>1993</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">On a ranking problem for symmetric and unimodal location parameter families</title><author xml:id="author-1"><persName><forename type="first">M.</forename><surname>Roters</surname></persName><note type="correspondence"><p>Correspondence to: M. 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Roters, Department of Mathematics and Statistics, University of Trier, W-5500 Trier, Germany.</ce:text></ce:correspondence></ce:author-group><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>Consider a location family of distributions generated by a symmetric and unimodal density w.r.t. Lebesgue measure. In this paper we prove that the probability of correctly ranking <ce:italic>k</ce:italic> = 3 populations from the above class of distributions subject to the condition that the range of the location parameters is bounded by 2δ is maximized for the parameter configuration (0, δ, 2δ). The corresponding conjecture that for <ce:italic>k</ce:italic> ⩾ 4 this maximum is also attained for the ‘equally spaced means configuration’ as above has, in general, a negative answer. A counterexample is given for <ce:italic>k</ce:italic> = 4 in the normal case.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Complete correct ranking</ce:text></ce:keyword><ce:keyword><ce:text>symmetric</ce:text></ce:keyword><ce:keyword><ce:text>unimodal density w.r.t. Lebesgue measure</ce:text></ce:keyword><ce:keyword><ce:text>equally spaced means configuration</ce:text></ce:keyword><ce:keyword><ce:text>Schur-concave function</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>On a ranking problem for symmetric and unimodal location parameter families</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>On a ranking problem for symmetric and unimodal location parameter families</title></titleInfo><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Roters</namePart><affiliation>University of Trier, Germany</affiliation><description>Correspondence to: M. Roters, Department of Mathematics and Statistics, University of Trier, W-5500 Trier, Germany.</description><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">1993</dateIssued><copyrightDate encoding="w3cdtf">1993</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">Consider a location family of distributions generated by a symmetric and unimodal density w.r.t. Lebesgue measure. In this paper we prove that the probability of correctly ranking k = 3 populations from the above class of distributions subject to the condition that the range of the location parameters is bounded by 2δ is maximized for the parameter configuration (0, δ, 2δ). The corresponding conjecture that for k ⩾ 4 this maximum is also attained for the ‘equally spaced means configuration’ as above has, in general, a negative answer. A counterexample is given for k = 4 in the normal case.</abstract><subject><genre>Keywords</genre><topic>Complete correct ranking</topic><topic>symmetric</topic><topic>unimodal density w.r.t. Lebesgue measure</topic><topic>equally spaced means configuration</topic><topic>Schur-concave function</topic></subject><relatedItem type="host"><titleInfo><title>Statistics and Probability Letters</title></titleInfo><titleInfo type="abbreviated"><title>STAPRO</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">19930104</dateIssued></originInfo><identifier type="ISSN">0167-7152</identifier><identifier type="PII">S0167-7152(00)X0172-1</identifier><part><date>19930104</date><detail type="volume"><number>16</number><caption>vol.</caption></detail><detail type="issue"><number>1</number><caption>no.</caption></detail><extent unit="issue pages"><start>1</start><end>83</end></extent><extent unit="pages"><start>47</start><end>49</end></extent></part></relatedItem><identifier type="istex">D61DC1EC421D23A29C5FB3A3D1659BFB36BB956B</identifier><identifier type="DOI">10.1016/0167-7152(93)90121-X</identifier><identifier type="PII">0167-7152(93)90121-X</identifier><recordInfo><recordContentSource>ELSEVIER</recordContentSource></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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