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ID:38337370
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页数:9页
时间:2019-06-10
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1、INFORMATIONCRITERIONANDCHANGEPOINTPROBLEMFORREGULARMODELSInformationcriteriaarecommonlyusedforselectingcompetingstatisticalmodels.Theydonotfavorthemodelwhichgivesthebesttothedataandlittleinterpretivevalue,butsimplermodelswithgoodfit.Thus,modelcomplexityisanimportantfactorininformationcriter
2、iaformodelselection.Existingresultsoftenequatethemodelcomplexitytothedimensionoftheparameterspace.Althoughthisnotioniswellfoundedinregularparametricmodels,itlackssomedesirablepropertieswhenappliedtoirregularstatisticalmodels.Werefinethenotionofmodelcomplexityinthecontextofchangepointproblem
3、s,andmodifytheexistinginformationcriteria.Themodifiedcriterionisfoundconsistentinselectingthecorrectmodelandhassimplelimitingbehavior.TheresultingestimatorofthelocationofthechangepointachievesthebestconvergencerateOp(1),anditslimitingdistributionisobtained.Simulationresultsindicatethatthemo
4、difiedcriterionhasbetterpowerindetectingchangescomparedtoothermethodsIntroductionOutofseveralcompetingstatisticalmodels,wedonotalwaysusetheonewiththebesttothedata.Suchmodelsmaysimplyinterpolatethedataandhavelittleinterpretivevalue.Informationcriteria,suchastheAkaikeinformationcriterionandth
5、eSchwarzinformationcriterion,aredesignedtoselectmodelswithsimplestructureandgoodinterpretivevalue,seeAkaike(1973)andSchwarz(1978).Themodelcomplexityisoftenmeasuredintermsofthedimensionalityoftheparameterspace.Considertheproblemofmakinginferenceonwhetheraprocesshasundergonesomechanges.Inthec
6、ontextofmodelselection,wewanttochoosebetweenamodelwithasinglesetofparameters,oramodelwithtwosetsofparametersplusthelocationofchange.TheAkaikeandtheSchwarzinformationcriteriacanbereadilyadoptedtothiskindofchangepointproblems.TherehavebeenmanyfruitfulresearchdoneinthisrespectsuchasHirotsu,Kur
7、ikiandHayter(1992)andChenandGupta(1997),tonameafew.Comparedtousualmodelselectionproblems,thechangepointproblemcontainsaspecialparameter:thelocationofthechange.Whenitapproachesthebeginningortheendoftheprocess,oneofthetwosetsoftheparameterbecomescompletely
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