Duality between multiple testing and selecting
Identifieur interne : 001A15 ( Istex/Corpus ); précédent : 001A14; suivant : 001A16Duality between multiple testing and selecting
Auteurs : H. Finner ; G. GianiSource :
- Journal of Statistical Planning and Inference [ 0378-3758 ] ; 1996.
Abstract
Selection problems are considered for which it is possible to formulate a correct selection via a so-called correct selection indicator. The correct selection indicator can be used to define a related multiple hypotheses testing problem. It is shown that there exists a bijective mapping from the class of all selection rules which guarantee a specified confidence level P∗ for a correct selection into a subfamily of all multiple tests at multiple level 1 − P∗. First of all, this correspondence may be of interest from a pure theoretical viewpoint. Moreover, methods developed for multiple hypotheses testing, such as the closure principle, sometimes allow considerable improvements of existing rules. Last but not least, the duality between multiple testing and selecting may yield a better understanding of the structure of the underlying decision problem. Three selection problems will be considered in more detail: subset selection of Gupta's type, best-or-all selection, and unrestricted subset selection. Application of the closure principle to Gupta's selection problem indicates that Gupta's rule cannot be improved. In fact, Gupta's rule turns out to be admissible in a certain sense. It is shown how the best-or-all selection problem can be treated by applying the duality results, and its connection to Bechhofer's indifference zone approach is pointed out in detail. The idea of stepwise multiple tests is adopted for the unrestricted subset selection problem. The primary task in the derivation of step-down procedures is the determination of least favorable parameter configurations with respect to certain hypotheses. The validity of the suggested step-up selection procedures depends on the validity of a conjecture concerning the critical values for these procedures. The step-up approach can be considered as a more informative extension of the best-or-all selection rule.
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DOI: 10.1016/0378-3758(95)00168-9
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title>Duality between multiple testing and selecting</title><author><name sortKey="Finner, H" sort="Finner, H" uniqKey="Finner H" first="H." last="Finner">H. Finner</name><affiliation><mods:affiliation>FB IV-Mathematik/Statistik, Universität Trier, D-54286 Trier, Germany</mods:affiliation></affiliation></author><author><name sortKey="Giani, G" sort="Giani, G" uniqKey="Giani G" first="G." last="Giani">G. Giani</name><affiliation><mods:affiliation>Corresponding author.</mods:affiliation></affiliation><affiliation><mods:affiliation>Abteilung Biometrie, Diabetes-Forschungsinstitut an der Universität Düsseldorf, Auf'm Hennekamp 65, D-40225 Düsseldorf, Germany</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:57211A3EC0607D25C78C7D25F8E049BF05437B24</idno><date when="1996" year="1996">1996</date><idno type="doi">10.1016/0378-3758(95)00168-9</idno><idno type="url">https://api.istex.fr/document/57211A3EC0607D25C78C7D25F8E049BF05437B24/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001A15</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001A15</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">Duality between multiple testing and selecting</title><author><name sortKey="Finner, H" sort="Finner, H" uniqKey="Finner H" first="H." last="Finner">H. Finner</name><affiliation><mods:affiliation>FB IV-Mathematik/Statistik, Universität Trier, D-54286 Trier, Germany</mods:affiliation></affiliation></author><author><name sortKey="Giani, G" sort="Giani, G" uniqKey="Giani G" first="G." last="Giani">G. Giani</name><affiliation><mods:affiliation>Corresponding author.</mods:affiliation></affiliation><affiliation><mods:affiliation>Abteilung Biometrie, Diabetes-Forschungsinstitut an der Universität Düsseldorf, Auf'm Hennekamp 65, D-40225 Düsseldorf, 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="1996">1996</date><biblScope unit="volume">54</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="201">201</biblScope><biblScope unit="page" to="227">227</biblScope></imprint><idno type="ISSN">0378-3758</idno></series><idno type="istex">57211A3EC0607D25C78C7D25F8E049BF05437B24</idno><idno type="DOI">10.1016/0378-3758(95)00168-9</idno><idno type="PII">0378-3758(95)00168-9</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">Selection problems are considered for which it is possible to formulate a correct selection via a so-called correct selection indicator. The correct selection indicator can be used to define a related multiple hypotheses testing problem. It is shown that there exists a bijective mapping from the class of all selection rules which guarantee a specified confidence level P∗ for a correct selection into a subfamily of all multiple tests at multiple level 1 − P∗. First of all, this correspondence may be of interest from a pure theoretical viewpoint. Moreover, methods developed for multiple hypotheses testing, such as the closure principle, sometimes allow considerable improvements of existing rules. Last but not least, the duality between multiple testing and selecting may yield a better understanding of the structure of the underlying decision problem. Three selection problems will be considered in more detail: subset selection of Gupta's type, best-or-all selection, and unrestricted subset selection. Application of the closure principle to Gupta's selection problem indicates that Gupta's rule cannot be improved. In fact, Gupta's rule turns out to be admissible in a certain sense. It is shown how the best-or-all selection problem can be treated by applying the duality results, and its connection to Bechhofer's indifference zone approach is pointed out in detail. The idea of stepwise multiple tests is adopted for the unrestricted subset selection problem. The primary task in the derivation of step-down procedures is the determination of least favorable parameter configurations with respect to certain hypotheses. The validity of the suggested step-up selection procedures depends on the validity of a conjecture concerning the critical values for these procedures. The step-up approach can be considered as a more informative extension of the best-or-all selection rule.</div></front></TEI><istex><corpusName>elsevier</corpusName><author><json:item><name>H. Finner</name><affiliations><json:string>FB IV-Mathematik/Statistik, Universität Trier, D-54286 Trier, Germany</json:string></affiliations></json:item><json:item><name>G. Giani</name><affiliations><json:string>Corresponding author.</json:string><json:string>Abteilung Biometrie, Diabetes-Forschungsinstitut an der Universität Düsseldorf, Auf'm Hennekamp 65, D-40225 Düsseldorf, Germany</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>62F07</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>62J15</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>62F03</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>62C15</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Admissibility of subset selection procedures</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Least favorable parameter configuration</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Multiple hypotheses testing</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Subset selection</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Step-down selection procedure</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Step-up selection procedure</value></json:item></subject><language><json:string>eng</json:string></language><originalGenre><json:string>Full-length article</json:string></originalGenre><abstract>Selection problems are considered for which it is possible to formulate a correct selection via a so-called correct selection indicator. The correct selection indicator can be used to define a related multiple hypotheses testing problem. It is shown that there exists a bijective mapping from the class of all selection rules which guarantee a specified confidence level P∗ for a correct selection into a subfamily of all multiple tests at multiple level 1 − P∗. First of all, this correspondence may be of interest from a pure theoretical viewpoint. Moreover, methods developed for multiple hypotheses testing, such as the closure principle, sometimes allow considerable improvements of existing rules. Last but not least, the duality between multiple testing and selecting may yield a better understanding of the structure of the underlying decision problem. Three selection problems will be considered in more detail: subset selection of Gupta's type, best-or-all selection, and unrestricted subset selection. Application of the closure principle to Gupta's selection problem indicates that Gupta's rule cannot be improved. In fact, Gupta's rule turns out to be admissible in a certain sense. It is shown how the best-or-all selection problem can be treated by applying the duality results, and its connection to Bechhofer's indifference zone approach is pointed out in detail. The idea of stepwise multiple tests is adopted for the unrestricted subset selection problem. The primary task in the derivation of step-down procedures is the determination of least favorable parameter configurations with respect to certain hypotheses. The validity of the suggested step-up selection procedures depends on the validity of a conjecture concerning the critical values for these procedures. The step-up approach can be considered as a more informative extension of the best-or-all selection rule.</abstract><qualityIndicators><score>8</score><pdfVersion>1.2</pdfVersion><pdfPageSize>461 x 684 pts</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>10</keywordCount><abstractCharCount>1892</abstractCharCount><pdfWordCount>11618</pdfWordCount><pdfCharCount>56252</pdfCharCount><pdfPageCount>27</pdfPageCount><abstractWordCount>284</abstractWordCount></qualityIndicators><title>Duality between multiple testing and selecting</title><pii><json:string>0378-3758(95)00168-9</json:string></pii><refBibs><json:item><author><json:item><name>P.O. Anderson</name></json:item><json:item><name>T.A. Bishop</name></json:item><json:item><name>E.J. Dudewicz</name></json:item></author><host><volume>6</volume><pages><last>1132</last><first>1121</first></pages><author></author><title>Comm. Statist. Theory Methods</title></host><title>Indifference-zone ranking and selection: confidence intervals for true achieved P(CD)</title></json:item><json:item><author><json:item><name>R.E. Bechhofer</name></json:item></author><host><volume>25</volume><pages><last>39</last><first>16</first></pages><author></author><title>Ann. Math. Statist.</title></host><title>A single-sample multiple decision procedure for ranking normal populations with known variances</title></json:item><json:item><author><json:item><name>R.E. Bechhofer</name></json:item></author><host><volume>5</volume><pages><last>233</last><first>201</first></pages><author></author><title>Amer. J. Math. Management Sci.</title></host><title>Selection and ranking procedures — some personal reminiscences, and thoughts about its past, present, and future</title></json:item><json:item><host><author></author><title>Sequential Identification and Ranking Procedures</title></host></json:item><json:item><author><json:item><name>E. Bofinger</name></json:item></author><host><volume>25</volume><pages><last>207</last><first>198</first></pages><author></author><title>Austral. J. Statist.</title></host><title>Multiple comparisons and selection</title></json:item><json:item><author><json:item><name>E. Bofinger</name></json:item></author><host><volume>29</volume><pages><last>364</last><first>348</first></pages><author></author><title>Austral. J. Statist.</title></host><title>Step down procedures for comparisons with a control</title></json:item><json:item><author><json:item><name>E. Bofinger</name></json:item></author><host><volume>17</volume><pages><last>1716</last><first>1697</first></pages><author></author><title>Comm. Statist. Theory Methods</title></host><title>Least significant spacing for ‘one versus the rest’ normal populations</title></json:item><json:item><author><json:item><name>E. Bofinger</name></json:item></author><host><volume>36</volume><pages><last>66</last><first>59</first></pages><author></author><title>Austral. J. Statist.</title></host><title>Should we estimate the probability of correct selection?</title></json:item><json:item><author><json:item><name>G. Broström</name></json:item></author><host><volume>10</volume><pages><last>221</last><first>203</first></pages><author></author><title>Comm. Statist. Theory Methods</title></host><title>On sequentially rejective subset selection procedures</title></json:item><json:item><author><json:item><name>L.D. Brown</name></json:item><json:item><name>H. Sackrowitz</name></json:item></author><host><volume>12</volume><pages><last>469</last><first>451</first></pages><author></author><title>Ann. Statist.</title></host><title>An alternative to Student's t-test for problems with indifference zones</title></json:item><json:item><author><json:item><name>S.G. Carmer</name></json:item><json:item><name>M.R. Swanson</name></json:item></author><host><volume>68</volume><pages><last>74</last><first>66</first></pages><author></author><title>J. Amer. Statist. Assoc.</title></host><title>An evaluation of ten multiple comparison procedures by Monte Carlo techniques</title></json:item><json:item><author><json:item><name>H.A. David</name></json:item><json:item><name>P.A. Lachenbruch</name></json:item><json:item><name>H.P. Brandis</name></json:item></author><host><volume>59</volume><pages><last>168</last><first>161</first></pages><author></author><title>Biometrika</title></host><title>The power function of range and studentised range tests in normal samples</title></json:item><json:item><author><json:item><name>C.W. Dunnett</name></json:item><json:item><name>A.C. Tamhane</name></json:item></author><host><volume>87</volume><pages><last>170</last><first>162</first></pages><author></author><title>J. Amer. Statist. Assoc.</title></host><title>A step-up multiple test procedure</title></json:item><json:item><author><json:item><name>H. Finner</name></json:item></author><host><volume>19</volume><pages><last>53</last><first>41</first></pages><author></author><title>Comm. Statist. Theory Methods</title></host><title>On the modified S-method and directional errors</title></json:item><json:item><author><json:item><name>H. Finner</name></json:item><json:item><name>G. Giani</name></json:item></author><host><volume>38</volume><pages><last>199</last><first>179</first></pages><author></author><title>J. Statist. Plann. Inference</title></host><title>Closed subset selection procedures for selecting good populations</title></json:item><json:item><author><json:item><name>H. Finner</name></json:item><json:item><name>A.J. Hayter</name></json:item><json:item><name>M. Roters</name></json:item></author><host><author></author><title>Technical Report Nr. 93-19</title></host><serie><author></author><title>Technical Report Nr. 93-19</title></serie><title>On the joint distribution of order statistics with reference to step-up multiple test procedures</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>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>K.R. Gabriel</name></json:item></author><host><volume>40</volume><pages><last>250</last><first>224</first></pages><author></author><title>Ann. Math. Statist.</title></host><title>Simultaneous test procedures — some theory of multiple comparisons</title></json:item><json:item><author><json:item><name>G. Giani</name></json:item><json:item><name>H. Finner</name></json:item></author><host><volume>28</volume><pages><last>47</last><first>33</first></pages><author></author><title>J. Statist. Plann. Inference</title></host><title>Some general results on least favorable parameter configurations with special reference to equivalence testing and the range statistic</title></json:item><json:item><author><json:item><name>G. Giani</name></json:item><json:item><name>K. Strassburger</name></json:item></author><host><volume>89</volume><pages><last>329</last><first>320</first></pages><author></author><title>J. Amer. Statist. Assoc.</title></host><title>Testing and selecting for equivalence with respect to a control</title></json:item><json:item><host><author></author><title>Selecting and Ordering Populations</title></host></json:item><json:item><author><json:item><name>S.S. Gupta</name></json:item></author><host><author></author><title>Mimeo Ser. No. 150</title></host><serie><author></author><title>Ph.D. Thesis</title></serie><title>On a decision rule for a problem in ranking means</title></json:item><json:item><author><json:item><name>S.S. Gupta</name></json:item></author><host><volume>7</volume><pages><last>245</last><first>225</first></pages><author></author><title>Technometrics</title></host><title>On some multiple decision (selection and ranking) rules</title></json:item><json:item><author><json:item><name>S.S. Gupta</name></json:item><json:item><name>L.Y. Leu</name></json:item><json:item><name>T. Liang</name></json:item></author><host><volume>19</volume><pages><last>546</last><first>527</first></pages><author></author><title>Comm. Statist. Theory Methods</title></host><title>On lower confidence bounds for PCS in truncated location parameter models</title></json:item><json:item><host><author></author><title>Multiple Decision Procedures: Theory and Methodology of Selecting and Ranking Populations</title></host></json:item><json:item><author><json:item><name>S. Gutmann</name></json:item><json:item><name>Z. Maymin</name></json:item></author><host><volume>15</volume><pages><last>461</last><first>456</first></pages><author></author><title>Ann. Statist.</title></host><title>Is the selected population the best?</title></json:item><json:item><host><author></author><title>Multiple Comparisons Procedures</title></host></json:item><json:item><author><json:item><name>J.C. Hsu</name></json:item></author><host><volume>9</volume><pages><last>1034</last><first>1026</first></pages><author></author><title>Ann. Statist.</title></host><title>Simultaneous confidence intervals for all distances with the ‘best’</title></json:item><json:item><author><json:item><name>J.C. Hsu</name></json:item></author><host><volume>12</volume><pages><last>1144</last><first>1136</first></pages><author></author><title>Ann. Statist.</title></host><title>Constrained simultaneous confidence intervals for multiple comparisons with the best</title></json:item><json:item><author><json:item><name>J.C. Hsu</name></json:item></author><host><volume>14</volume><pages><last>2028</last><first>2009</first></pages><author></author><title>Comm. Statist. Theory Methods</title></host><title>A method of unconstrained multiple comparisons with the best</title></json:item><json:item><author><json:item><name>J.C. Hsu</name></json:item></author><host><volume>33</volume><pages><last>204</last><first>197</first></pages><author></author><title>J. Statist. Plann. Inference</title></host><title>Stepwise multiple comparisons with the best</title></json:item><json:item><author><json:item><name>W.-C. Kim</name></json:item></author><host><volume>81</volume><pages><last>1017</last><first>1012</first></pages><author></author><title>J. Amer. Statist. Assoc.</title></host><title>A lower confidence bound on the probability of a correct selection</title></json:item><json:item><author><json:item><name>K. Lam</name></json:item></author><host><volume>73</volume><pages><last>206</last><first>201</first></pages><author></author><title>Biometrika</title></host><title>A new procedure for selecting good populations</title></json:item><json:item><author><json:item><name>E.L. Lehmann</name></json:item></author><host><volume>28</volume><pages><last>572</last><first>547</first></pages><author></author><title>Ann. Math. Statist.</title></host><title>A theory of some multiple decision problems — part I</title></json:item><json:item><author><json:item><name>R. Marcus</name></json:item><json:item><name>E. Peritz</name></json:item><json:item><name>K.R. Gabriel</name></json:item></author><host><volume>63</volume><pages><last>660</last><first>655</first></pages><author></author><title>Biometrika</title></host><title>On closed testing procedures with special reference to ordered analysis of variance</title></json:item><json:item><author><json:item><name>Z. Mayman</name></json:item><json:item><name>S. Gutmann</name></json:item></author><host><volume>20</volume><pages><last>345</last><first>335</first></pages><author></author><title>Canad. J. Statist.</title></host><title>Testing retrospective hypotheses</title></json:item><json:item><author><json:item><name>K.J. Miescke</name></json:item></author><host><volume>7</volume><pages><last>219</last><first>207</first></pages><author></author><title>Ann. Statist.</title></host><title>Identification and selection procedures based on tests</title></json:item><json:item><host><author></author><title>Simultaneous Statistical Inference</title></host></json:item><json:item><author><json:item><name>U.D. Naik</name></json:item></author><host><volume>4</volume><pages><last>535</last><first>519</first></pages><author></author><title>Comm. Statist.</title></host><title>Some selection rules for comparing p processes with a standard</title></json:item><json:item><author><json:item><name>U.D. Naik</name></json:item></author><host><volume>6</volume><pages><last>966</last><first>955</first></pages><author></author><title>Comm. Statist. Theory Methods</title></host><title>Some subset selection problems</title></json:item><json:item><author><json:item><name>J.P.Du Preez</name></json:item><json:item><name>J.W.H. Swanepoel</name></json:item><json:item><name>J.H. Venter</name></json:item><json:item><name>P.N. Somerville</name></json:item></author><host><volume>19</volume><pages><last>125</last><first>115</first></pages><author></author><title>South African Statist. J.</title></host><title>Procedures with lower expected subset size than that of Gupta's subset selection procedure for three normal populations</title></json:item><json:item><author><json:item><name>J.P.Du Preez</name></json:item><json:item><name>J.W.H. Swanepoel</name></json:item><json:item><name>J.H. Venter</name></json:item><json:item><name>P.N. Somerville</name></json:item></author><host><volume>19</volume><pages><last>72</last><first>45</first></pages><author></author><title>South African Statist. J.</title></host><title>Some properties of Somerville's multiple range subset selection procedure for three populations</title></json:item><json:item><author><json:item><name>A. Prekopa</name></json:item></author><host><volume>36</volume><pages><last>343</last><first>335</first></pages><author></author><title>Acta Sci. Math. (Szeged)</title></host><title>On logarithmic concave measures and functions</title></json:item><json:item><author><json:item><name>D.M. Rom</name></json:item></author><host><volume>77</volume><pages><last>665</last><first>663</first></pages><author></author><title>Biometrika</title></host><title>A sequentially rejective test procedure based on a modified Bonferroni inequality</title></json:item><json:item><author><json:item><name>P.N. Somerville</name></json:item></author><host><volume>19</volume><pages><last>226</last><first>215</first></pages><author></author><title>J. Statist. Comput. Simulation</title></host><title>A multiple range subset selection procedure</title></json:item><json:item><author><json:item><name>P.N. Somerville</name></json:item></author><host><volume>22</volume><pages><last>50</last><first>27</first></pages><author></author><title>J. Statist. Comput. Simulation</title></host><title>A new subset selection method for normal populations</title></json:item><json:item><author><json:item><name>P.N. Somerville</name></json:item></author><host><pages><last>89</last><first>85</first></pages><author></author><title>The Frontiers of Modern Statistical Inference Procedures, Proc. and Discussions of the IPASRAS Conference</title></host><title>A subset selection procedure for three normal populations (with discussion)</title></json:item><json:item><author><json:item><name>P.N. Somerville</name></json:item></author><host><volume>6</volume><pages><last>184</last><first>169</first></pages><author></author><title>Amer. J. Math. Management Sci.</title></host><title>On the geometry of some subset selection procedures</title></json:item><json:item><author><json:item><name>E. Sonnemann</name></json:item><json:item><name>H. Finner</name></json:item></author><host><pages><last>135</last><first>121</first></pages><author></author><title>Multiple Hypothesenprüfung — Multiple Hypotheses Testing</title></host><title>Vollständigkeitssätze für multiple Testprobleme (Complete class theorems for testing multiple hypotheses)</title></json:item><json:item><author><json:item><name>G. Stefansson</name></json:item><json:item><name>W.-C. Kim</name></json:item><json:item><name>J.C. Hsu</name></json:item></author><host><author></author><title>Statistical Decision Theory and related Topics</title></host><serie><author></author><title>Statistical Decision Theory and related Topics</title></serie><title>On confidence sets in multiple comparisons</title></json:item><json:item><author><json:item><name>R.E. Welsch</name></json:item></author><host><volume>72</volume><pages><last>575</last><first>566</first></pages><author></author><title>J. Amer. Statist. Assoc.</title></host><title>Stepwise multiple comparison procedures</title></json:item><json:item><author><json:item><name>P.H. Westfall</name></json:item><json:item><name>S.S. Young</name></json:item></author><host><author></author><title>Examples and Methods for p-value Adjustment</title></host><title>Resampling-based Multiple Testing</title></json:item></refBibs><genre><json:string>research-article</json:string></genre><serie><language><json:string>unknown</json:string></language><title>Technical Report Nr. 93-19</title></serie><host><volume>54</volume><pii><json:string>S0378-3758(00)X0026-2</json:string></pii><pages><last>227</last><first>201</first></pages><issn><json:string>0378-3758</json:string></issn><issue>2</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>Journal of Statistical Planning and Inference</title><publicationDate>1996</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>1996</publicationDate><copyrightDate>1996</copyrightDate><doi><json:string>10.1016/0378-3758(95)00168-9</json:string></doi><id>57211A3EC0607D25C78C7D25F8E049BF05437B24</id><score>0.5872945</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/57211A3EC0607D25C78C7D25F8E049BF05437B24/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/57211A3EC0607D25C78C7D25F8E049BF05437B24/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/57211A3EC0607D25C78C7D25F8E049BF05437B24/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Duality between multiple testing and selecting</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>ELSEVIER</publisher><availability><p>ELSEVIER</p></availability><date>1996</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">Duality between multiple testing and selecting</title><author xml:id="author-1"><persName><forename type="first">H.</forename><surname>Finner</surname></persName><affiliation>FB IV-Mathematik/Statistik, Universität Trier, D-54286 Trier, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">G.</forename><surname>Giani</surname></persName><affiliation>Corresponding author.</affiliation><affiliation>Abteilung Biometrie, Diabetes-Forschungsinstitut an der Universität Düsseldorf, Auf'm Hennekamp 65, D-40225 Düsseldorf, 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)X0026-2</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1996"></date><biblScope unit="volume">54</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="201">201</biblScope><biblScope unit="page" to="227">227</biblScope></imprint></monogr><idno type="istex">57211A3EC0607D25C78C7D25F8E049BF05437B24</idno><idno type="DOI">10.1016/0378-3758(95)00168-9</idno><idno type="PII">0378-3758(95)00168-9</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1996</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Selection problems are considered for which it is possible to formulate a correct selection via a so-called correct selection indicator. The correct selection indicator can be used to define a related multiple hypotheses testing problem. It is shown that there exists a bijective mapping from the class of all selection rules which guarantee a specified confidence level P∗ for a correct selection into a subfamily of all multiple tests at multiple level 1 − P∗. First of all, this correspondence may be of interest from a pure theoretical viewpoint. Moreover, methods developed for multiple hypotheses testing, such as the closure principle, sometimes allow considerable improvements of existing rules. Last but not least, the duality between multiple testing and selecting may yield a better understanding of the structure of the underlying decision problem. Three selection problems will be considered in more detail: subset selection of Gupta's type, best-or-all selection, and unrestricted subset selection. Application of the closure principle to Gupta's selection problem indicates that Gupta's rule cannot be improved. In fact, Gupta's rule turns out to be admissible in a certain sense. It is shown how the best-or-all selection problem can be treated by applying the duality results, and its connection to Bechhofer's indifference zone approach is pointed out in detail. The idea of stepwise multiple tests is adopted for the unrestricted subset selection problem. The primary task in the derivation of step-down procedures is the determination of least favorable parameter configurations with respect to certain hypotheses. The validity of the suggested step-up selection procedures depends on the validity of a conjecture concerning the critical values for these procedures. The step-up approach can be considered as a more informative extension of the best-or-all selection rule.</p></abstract><textClass><keywords scheme="keyword"><list><head>MSC</head><item><term>62F07</term></item><item><term>62J15</term></item></list></keywords></textClass><textClass><keywords scheme="keyword"><list><head>MSC</head><item><term>62F03</term></item><item><term>62C15</term></item></list></keywords></textClass><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>Admissibility of subset selection procedures</term></item><item><term>Least favorable parameter configuration</term></item><item><term>Multiple hypotheses testing</term></item><item><term>Subset selection</term></item><item><term>Step-down selection procedure</term></item><item><term>Step-up selection procedure</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1995-04-19">Modified</change><change when="1996">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/57211A3EC0607D25C78C7D25F8E049BF05437B24/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: 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>95001689</aid><ce:pii>0378-3758(95)00168-9</ce:pii><ce:doi>10.1016/0378-3758(95)00168-9</ce:doi><ce:copyright type="unknown" year="1996"></ce:copyright></item-info><head><ce:title>Duality between multiple testing and selecting</ce:title><ce:author-group><ce:author><ce:given-name>H.</ce:given-name><ce:surname>Finner</ce:surname><ce:cross-ref refid="AFF1"><ce:sup>a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>G.</ce:given-name><ce:surname>Giani</ce:surname><ce:cross-ref refid="COR1"><ce:sup>∗</ce:sup></ce:cross-ref><ce:cross-ref refid="AFF2"><ce:sup>b</ce:sup></ce:cross-ref></ce:author><ce:affiliation id="AFF1"><ce:label>a</ce:label><ce:textfn>FB IV-Mathematik/Statistik, Universität Trier, D-54286 Trier, Germany</ce:textfn></ce:affiliation><ce:affiliation id="AFF2"><ce:label>b</ce:label><ce:textfn>Abteilung Biometrie, Diabetes-Forschungsinstitut an der Universität Düsseldorf, Auf'm Hennekamp 65, D-40225 Düsseldorf, Germany</ce:textfn></ce:affiliation><ce:correspondence id="COR1"><ce:label>∗</ce:label><ce:text>Corresponding author.</ce:text></ce:correspondence></ce:author-group><ce:date-received day="1" month="3" year="1994"></ce:date-received><ce:date-revised day="19" month="4" year="1995"></ce:date-revised><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>Selection problems are considered for which it is possible to formulate a correct selection via a so-called correct selection indicator. The correct selection indicator can be used to define a related multiple hypotheses testing problem. It is shown that there exists a bijective mapping from the class of all selection rules which guarantee a specified confidence level <math altimg="si1.gif">P∗</math> for a correct selection into a subfamily of all multiple tests at multiple level <math altimg="si2.gif">1 − P∗</math>. First of all, this correspondence may be of interest from a pure theoretical viewpoint. Moreover, methods developed for multiple hypotheses testing, such as the closure principle, sometimes allow considerable improvements of existing rules. Last but not least, the duality between multiple testing and selecting may yield a better understanding of the structure of the underlying decision problem. Three selection problems will be considered in more detail: subset selection of Gupta's type, best-or-all selection, and unrestricted subset selection. Application of the closure principle to Gupta's selection problem indicates that Gupta's rule cannot be improved. In fact, Gupta's rule turns out to be admissible in a certain sense. It is shown how the best-or-all selection problem can be treated by applying the duality results, and its connection to Bechhofer's indifference zone approach is pointed out in detail. The idea of stepwise multiple tests is adopted for the unrestricted subset selection problem. The primary task in the derivation of step-down procedures is the determination of least favorable parameter configurations with respect to certain hypotheses. The validity of the suggested step-up selection procedures depends on the validity of a conjecture concerning the critical values for these procedures. The step-up approach can be considered as a more informative extension of the best-or-all selection rule.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords class="msc"><ce:section-title>MSC</ce:section-title><ce:keyword><ce:text>62F07</ce:text></ce:keyword><ce:keyword><ce:text>62J15</ce:text></ce:keyword></ce:keywords><ce:keywords class="msc"><ce:section-title>MSC</ce:section-title><ce:keyword><ce:text>62F03</ce:text></ce:keyword><ce:keyword><ce:text>62C15</ce:text></ce:keyword></ce:keywords><ce:keywords><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Admissibility of subset selection procedures</ce:text></ce:keyword><ce:keyword><ce:text>Least favorable parameter configuration</ce:text></ce:keyword><ce:keyword><ce:text>Multiple hypotheses testing</ce:text></ce:keyword><ce:keyword><ce:text>Subset selection</ce:text></ce:keyword><ce:keyword><ce:text>Step-down selection procedure</ce:text></ce:keyword><ce:keyword><ce:text>Step-up selection procedure</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Duality between multiple testing and selecting</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Duality between multiple testing and selecting</title></titleInfo><name type="personal"><namePart type="given">H.</namePart><namePart type="family">Finner</namePart><affiliation>FB IV-Mathematik/Statistik, Universität Trier, D-54286 Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">G.</namePart><namePart type="family">Giani</namePart><affiliation>Corresponding author.</affiliation><affiliation>Abteilung Biometrie, Diabetes-Forschungsinstitut an der Universität Düsseldorf, Auf'm Hennekamp 65, D-40225 Düsseldorf, 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">1996</dateIssued><dateModified encoding="w3cdtf">1995-04-19</dateModified><copyrightDate encoding="w3cdtf">1996</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">Selection problems are considered for which it is possible to formulate a correct selection via a so-called correct selection indicator. The correct selection indicator can be used to define a related multiple hypotheses testing problem. It is shown that there exists a bijective mapping from the class of all selection rules which guarantee a specified confidence level P∗ for a correct selection into a subfamily of all multiple tests at multiple level 1 − P∗. First of all, this correspondence may be of interest from a pure theoretical viewpoint. Moreover, methods developed for multiple hypotheses testing, such as the closure principle, sometimes allow considerable improvements of existing rules. Last but not least, the duality between multiple testing and selecting may yield a better understanding of the structure of the underlying decision problem. Three selection problems will be considered in more detail: subset selection of Gupta's type, best-or-all selection, and unrestricted subset selection. Application of the closure principle to Gupta's selection problem indicates that Gupta's rule cannot be improved. In fact, Gupta's rule turns out to be admissible in a certain sense. It is shown how the best-or-all selection problem can be treated by applying the duality results, and its connection to Bechhofer's indifference zone approach is pointed out in detail. The idea of stepwise multiple tests is adopted for the unrestricted subset selection problem. The primary task in the derivation of step-down procedures is the determination of least favorable parameter configurations with respect to certain hypotheses. The validity of the suggested step-up selection procedures depends on the validity of a conjecture concerning the critical values for these procedures. The step-up approach can be considered as a more informative extension of the best-or-all selection rule.</abstract><subject><genre>MSC</genre><topic>62F07</topic><topic>62J15</topic></subject><subject><genre>MSC</genre><topic>62F03</topic><topic>62C15</topic></subject><subject><genre>Keywords</genre><topic>Admissibility of subset selection procedures</topic><topic>Least favorable parameter configuration</topic><topic>Multiple hypotheses testing</topic><topic>Subset selection</topic><topic>Step-down selection procedure</topic><topic>Step-up selection procedure</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">19960916</dateIssued></originInfo><identifier type="ISSN">0378-3758</identifier><identifier type="PII">S0378-3758(00)X0026-2</identifier><part><date>19960916</date><detail type="issue"><title>40 Years of Statistical Selection Theory, Part I</title></detail><detail type="volume"><number>54</number><caption>vol.</caption></detail><detail type="issue"><number>2</number><caption>no.</caption></detail><extent unit="issue pages"><start>141</start><end>244</end></extent><extent unit="pages"><start>201</start><end>227</end></extent></part></relatedItem><identifier type="istex">57211A3EC0607D25C78C7D25F8E049BF05437B24</identifier><identifier type="DOI">10.1016/0378-3758(95)00168-9</identifier><identifier type="PII">0378-3758(95)00168-9</identifier><recordInfo><recordContentSource>ELSEVIER</recordContentSource></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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