Ⅰ型區(qū)間刪失情形下競爭風(fēng)險混合參數(shù)模型極大似然估計漸近性研究.pdf

1、大連理工大學(xué)碩士學(xué)位論文Ⅰ型區(qū)間刪失情形下競爭風(fēng)險混合參數(shù)模型極大似然估計漸近性研究姓名：胡濤申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：賀明峰20060601ASYMPTICPROPERTIES0FPARAMETR_ICMoDEL’SMLEFoRCoMPETINGRISKSⅥⅡTHCURRENTSTATUSDATAAbstractTheanalysisofcompetingrisksdatagoestotheheartofmodernp

2、reoccupationsinsurvivalanalysis。touching嬲itdoesonmanyofthemajoraressofimportanceinthesubjectT11eclassificationofdeathorfailureby“type”or“cause”isanaturalextensionoffsinglecause)survivalanalysis，onceweconsideralternativeo

3、r“competing”causesofdeathorfailureTheeffortexpendedinfittingandinterpretingcompetingrisksmodelsofsomesort，evidentfromaglanceatthecurrentliterature，recommendsthemasaworthwhileobjectofstudySee，forexample，LarsonandDinse(198

4、5)，DavidandMoeschberger(1978)，KalbfleischandPrentice(1980)，Gaynoreta1(1993)，Escarela，F(xiàn)rancisandSoothiU(2000)，Tai，Machin，WhiteandGebski(2001)，andtheirreferencesWhiletherehavebeenmanyinvestigations，oftenfromthepointofviewo

5、fcountingprocesstheory(eg，Andersen，Borgan，GillandKeiding(1993)，F(xiàn)lemingandHarrington(1991)，KalbflcischandPrentice(1980))，ofpropertiesofvariousformulationsofcompetingrisksroodelsacomprehensivelargesampleanalysisofcertainin

6、terestingaspectshasbeengiveⅡSOfarAclassof“mixturemodels”，usedforexampleinapaperbyLarsonandDinse(1985)(seealsoElandt—JohnsonandJohnson(1980，p288)，whichplaysaprominentroleintheanalysisofcompetingrisksanddirectlyaddressesth

7、edataanalyticquestionsofinterestTofillthisneedweprovidearigorousanedysisoftheparametricmixturemodelsandderiveusefullargesamplepropertiesofmaximumlikelihoodestimatorsSomeoftheparametersofinterestinthemodel，namelythemixing

8、probabilities，areconstrainedtoaJdimensionalsimplex，andoneoftheinterestinghypothesesrequiresthoseparameterstolieonthefaceofthesimplexUnderrightcensormodel，MailerandXianZhouprovidearigorousanalysisoftheparametricmixturemod

9、elsandderiveusefullarge—samplepropertiesofmaximumlikelihoodestimatorsandteststatistics，whichcoverbothinteriorandboundarycases’Thisstudyproposesamethodofcomputingthemaximumlikelihoodestimator(MLE)ofparametersunderthenonne

10、gativerestrictionAsimilarmethodisalsoproposedforthecasewheretheparameters8rerestrictedbyasimpleorderUnderaniidcurrentstatusdatamodel，whentheparametersareintheinterioroftheparameterspace，weshowthatthemixturemodelapproachp