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1、LinearModelSelectionbyCross-ValidationAuthor(s):JunShaoSource:JournaloftheAmericanStatisticalAssociation,Vol.88,No.422(Jun.,1993),pp.486-494Publishedby:AmericanStatisticalAssociationStableURL:http://www.jstor.org/stable/2290328.Accessed:31/03/201323:39Yourus
2、eoftheJSTORarchiveindicatesyouracceptanceoftheTerms&ConditionsofUse,availableat.http://www.jstor.org/page/info/about/policies/terms.jsp.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrust
3、eddigitalarchive.Weuseinformationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org..AmericanStatisticalAssociationiscollaboratingwithJSTORtodigitize,preserveandextendaccesst
4、oJournaloftheAmericanStatisticalAssociation.http://www.jstor.orgThiscontentdownloadedfrom147.8.105.97onSun,31Mar201323:39:04PMAllusesubjecttoJSTORTermsandConditionsLinearModelSelectionbyCross-ValidationJUNSHAO*Weconsidertheproblemofselectingamodelhavingthebe
5、stpredictiveabilityamongaclassoflinearmodels.Thepopularleave-one-outcross-validationmethod,whichisasymptoticallyequivalenttomanyothermodelselectionmethodssuchastheAkaikeinformationcriterion(AIC),theCp,andthebootstrap,isasymptoticallyinconsistentinthesensetha
6、ttheprobabilityofselectingthemodelwiththebestpredictiveabilitydoesnotconvergeto1asthetotalnumberofobservationsn-so.Weshowthattheinconsistencyoftheleave-one-outcross-validationcanberectifiedbyusingaleave-n,-outcross-validationwithnv,thenumberofobservationsres
7、ervedforvalidation,satisfyingno/n-1Iasns*xoo.Thisisasomewhatshockingdiscovery,becausene/n-*1istotallyoppositetothepopularleave-one-outrecipeincross-validation.Motivations,justifications,anddiscussionsofsomepracticalaspectsoftheuseoftheleave-n,-outcross-valid
8、ationmethodareprovided,andresultsfromasimulationstudyarepresented.KEYWORDS:Balancedincomplete;Consistency;Datasplitting;Modelassessment;MonteCarlo;Prediction.1.INTRODUCTION(dependingonn).Ourresu
