variable selection in robust joint mean andcovariance model for longitudinal data analysis

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1、StatisticaSinica24(2014),515-531doi:http://dx.doi.org/10.5705/ss.2011.251VARIABLESELECTIONINROBUSTJOINTMEANANDCOVARIANCEMODELFORLONGITUDINALDATAANALYSISXueyingZheng1,WingKamFung2andZhongyiZhu11FudanUniversityand2TheUniversityofHongKongAbstract:Inlongitudinaldataanalysis,acorrectspecificationofthewith

2、in-subjectcovariancematrixcultivatesanefficientestimationformeanregressioncoefficients.Inthisarticle,weconsiderrobustvariableselectionmethodinajointmeanandcovariancemodel.Weproposeasetofpenalizedrobustgeneralizedestimatingequationstosimultaneouslyestimatethemeanregressioncoefficients,thegeneral-izedautore

3、gressivecoefficients,andinnovationvariancesintroducedbythemodifiedCholeskydecomposition.Thesetofestimatingequationsselectimportantcovari-atevariablesinbothmeanandcovariancemodelstogetherwiththeestimatingprocedure.Undersomeregularityconditions,wedeveloptheoraclepropertyoftheproposedrobustvariableselecti

4、onmethod.Finally,asimulationstudyandadetaileddataanalysisarecarriedouttoassessandillustratethesmallsampleper-formance;theyshowthattheproposedmethodperformsfavorablybycombiningtherobustifyingandpenalizedestimatingtechniquestogetherinthejointmeanandcovariancemodel.Keywordsandphrases:Covariancematrix,p

5、enalizedgeneralizedestimatingequa-tion,longitudinaldata,modifiedcholeskydecomposition,robustness,variablese-lection.1.IntroductionLongitudinaldataarisemoreandmorefrequentlyinavarietyofscientificdomainsthatseekinsightfulandcomprehensiveresearchinabranchofstatisti-calmodeling.Differentfromothertypesofdat

6、a,weoftenassumeindependenceamongdistinctsubjectsbutdependencewithineachsubject;within-subjectcor-relationraisesafundamentalchallengefortheanalysisoflongitudinaldata.LiangandZeger(1986),amilestoneinthedevelopmentofmethodologyforlongitudinaldataanalysis,proposedgeneralizedestimatingequations(GEE)fores

7、timationofgeneralizedlinearregressioncoefficients.Themainadvantageoftheirmethodisthatevenwhenthewithin-subjectcorrelationistreatedasanuisanceparameterwithanassumedparsimoniousstructure,GEEstillbringsabo