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1、WeightedSemiparametricEstimationinRegressionAnalysisWithMissingCovariateDataC.Y.WANG,SuojinWANG,Lue-PingZHAO,andShyh-TyanOuThisarticleinvestigatesestimationoftheregressioncoefficientsinanassumedmeanfunctionwhencovariatesonsomesubjectsaremissing.WeexaminetheperformanceofaHorvitzan
2、dThompson(1952)-typeweightedestimatorbyusingdifferentestimatesoftheselectionprobabilities,whichmaybetreatedasnuisanceparameters(oranuisancefunction).Inparticular,weinvestigatethepropertiesoftheestimateoftheregressionparameterswhentheselectionprobabilitiesareestimatedbykernelsmoot
3、hers.Wepresentlargesampletheoryforthenewestimatorandconductsimulationstudiescomparingtheproposedestimatortothemaximumlikelihoodestimatorandmultipleimputationundervariousmodelassumptionsanddifferentmissingnessmechanisms.Inaddition,weprovidetworealexamplesthatmotivatethisinvestigat
4、ion.KEYWORDS:Case-controlstudy;Estimatingequation;Kernelsmoother;Logisticregression;Measurementerrormodel;Missingatrandom.1.INTRODUCTIONorbylinearregressiononZ'sandY's(Buck1960)fromthecompletecases.Rubin(1978,1987)proposedmultipleTheanalysisofmissingcovariatedataisapracticalimput
5、ationasasolutiontotheproblem.TheEMalgorithmandinterestingproblemintheregressionanalysisofa(Dempster,Laird,andRubin1977)givesausefultoolforunivariateresponse,Y,onavectorofcovariates(X,Z),maximumlikelihoodestimationwhenitrequiresiterativewherethecovariateXmaybemissingpartiallyonasu
6、b-methods.setofrecords.Forexample,inacase-controlstudyofAcloselyrelatedproblemariseswhenXismeasureddietandthyroidcancerconductedinHawaii,39subjectswitherrorandasurrogatevariableforXisavailable.Sev-(totaln=468)hadtheiraveragedailytotaliodinein-eralmethodshavebeenproposed.Forexampl
7、e,Breslowtakesmissing.Anotherexample,illustratedlaterinthisandCain(1988)haveproposedapseudo-conditionallike-article,isacase-controlstudyofesophagusandgastriclihoodmethodfortwo-stagecase-controlstudies.WhencardiacancersinwesternWashingtonstate,whereaboutmissingnessdoesnotdependone
8、itherYorX,Carrollandone-thirdofthesubjec
