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Article: A predictive approach for the selection of a fixed number of good treatments

TitleA predictive approach for the selection of a fixed number of good treatments
Authors
KeywordsRanking and selection
predictive approach
correct selection
predictive bounds
simultaneous control
Issue Date1994
PublisherTaylor & Francis Inc. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/03610926.asp
Citation
Communications in Statistics: Theory and Methods, 1994, v. 23 n. 9, p. 2469-2492 How to Cite?
AbstractThis paper offers a predictive approach for the selection of a fixed number (= t) of treatments from k treatments with the goal of controlling for predictive losses. For the ith treatment, independent observations X(ij) (j = 1, 2, ..., n) can be observed where X(ij)'s are normally distributed N(theta(i);sigma2). The ranked values of theta(i)'s and X(i)BAR's are theta(1) less-than-or-equal-to ... less-than-or-equal-to theta((k)) and X[1]BAR less-than-or-equal-to ... less-than-or-equal-to X[k]BAR and the selected subset S = {[k], [k - 1], ... , [k - t + 1]) will be considered. This paper distinguishes between two types of loss functions. A type I loss function associated with a selected subset S is the loss in utility from the selector's view point and is a function of theta(i) with i is-an-element-of S. A type II loss function associated with S measures the unfairness in the selection from candidates' viewpoint and is a function of theta(i) with i is-an-element-of S. This paper shows that under mild assumptions on the loss functions S is optimal and provides the necessary formulae for choosing n so that the two types of loss can be controlled individually or simultaneously with a high probability. Predictive bounds for the losses are provided. Numerical examples support the usefulness of the predictive approach over the design of experiment approach.
Persistent Identifierhttp://hdl.handle.net/10722/82812
ISSN
2015 Impact Factor: 0.3
2015 SCImago Journal Rankings: 0.518

 

DC FieldValueLanguage
dc.contributor.authorLam, Ken_HK
dc.contributor.authorYu, PLHen_HK
dc.date.accessioned2010-09-06T08:33:42Z-
dc.date.available2010-09-06T08:33:42Z-
dc.date.issued1994en_HK
dc.identifier.citationCommunications in Statistics: Theory and Methods, 1994, v. 23 n. 9, p. 2469-2492en_HK
dc.identifier.issn0361-0926en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82812-
dc.description.abstractThis paper offers a predictive approach for the selection of a fixed number (= t) of treatments from k treatments with the goal of controlling for predictive losses. For the ith treatment, independent observations X(ij) (j = 1, 2, ..., n) can be observed where X(ij)'s are normally distributed N(theta(i);sigma2). The ranked values of theta(i)'s and X(i)BAR's are theta(1) less-than-or-equal-to ... less-than-or-equal-to theta((k)) and X[1]BAR less-than-or-equal-to ... less-than-or-equal-to X[k]BAR and the selected subset S = {[k], [k - 1], ... , [k - t + 1]) will be considered. This paper distinguishes between two types of loss functions. A type I loss function associated with a selected subset S is the loss in utility from the selector's view point and is a function of theta(i) with i is-an-element-of S. A type II loss function associated with S measures the unfairness in the selection from candidates' viewpoint and is a function of theta(i) with i is-an-element-of S. This paper shows that under mild assumptions on the loss functions S is optimal and provides the necessary formulae for choosing n so that the two types of loss can be controlled individually or simultaneously with a high probability. Predictive bounds for the losses are provided. Numerical examples support the usefulness of the predictive approach over the design of experiment approach.-
dc.languageengen_HK
dc.publisherTaylor & Francis Inc. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/03610926.aspen_HK
dc.relation.ispartofCommunications in Statistics: Theory and Methodsen_HK
dc.rightsThis is an electronic version of an article published in [include the complete citation information for the final version of the article as published in the print edition of the journal]. [JOURNAL TITLE] is available online at: http://www.informaworld.com/smpp/ with the open URL of your article.-
dc.subjectRanking and selection-
dc.subjectpredictive approach-
dc.subjectcorrect selection-
dc.subjectpredictive bounds-
dc.subjectsimultaneous control-
dc.titleA predictive approach for the selection of a fixed number of good treatmentsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0361-0926&volume=23&issue=9&spage=2469&epage=2492&date=1994&atitle=A+predictive+approach+for+the+selection+of+a+fixed+number+of+good+treatmentsen_HK
dc.identifier.emailLam, K: hrntlam@hkucc.hku.hken_HK
dc.identifier.emailYu, PLH: plhyu@hkucc.hku.hken_HK
dc.identifier.hkuros8662en_HK
dc.identifier.volume23-
dc.identifier.issue9-
dc.identifier.spage2469-
dc.identifier.epage2492-

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