简介:Linearmixedmodels(LMMs)havebecomeanimportantstatisticalmethodforanalyzingclusterorlongitudinaldata.Inmostcases,itisassumedthatthedistributionsoftherandomeffectsandtheerrorsarenormal.Thispaperremovesthisrestrictionsandreplacethembythemomentconditions.WeshowthattheleastsquareestimatorsoffixedeffectsareconsistentandasymptoticallynormalingeneralLMMs.Aclosed-formestimatorofthecovariancematrixfortherandomeffectisconstructedanditsconsistentisshown.Basedonthis,theconsistentestimatefortheerrorvarianceisalsoobtained.Asimulationstudyandarealdataanalysisshowthattheprocedureiseffective.
简介:Receiveroperatingcharacteristic(ROC)curvesareoftenusedtostudythetwosampleprobleminmedicalstudies.However,mostdatainmedicalstudiesarecensored.UsuallyanaturalestimatorisbasedontheKaplan-Meierestimator.InthispaperweproposeasmoothedestimatorbasedonkerneltechniquesfortheROCcurvewithcensoreddata.Thelargesamplepropertiesofthesmoothedestimatorareestablished.Moreover,deficiencyisconsideredinordertocomparetheproposedsmoothedestimatoroftheROCcurvewiththeempiricalonebasedonKaplan-Meierestimator.ItisshownthatthesmoothedestimatoroutperformsthedirectempiricalestimatorbasedontheKaplan-Meierestimatorunderthecriterionofdeficiency.Asimulationstudyisalsoconductedandarealdataisanalyzed.
简介:Totacklemulticollinearityorill-conditioneddesignmatricesinlinearmodels,adaptivebiasedestimatorssuchasthetime-honoredSteinestimator,theridgeandtheprincipalcomponentestimatorshavebeenstudiedintensively.Tostudywhenabiasedestimatoruniformlyoutperformstheleastsquaresestimator,somesufficientconditionsareproposedintheliterature.Inthispaper,weproposeaunifiedframeworktoformulateaclassofadaptivebiasedestimators.Thisclassincludesallexistingbiasedestimatorsandsomenewones.Asufficientconditionforoutperformingtheleastsquaresestimatorisproposed.Intermsofselectingparametersinthecondition,wecanobtainalldouble-typeconditionsintheliterature.
简介:§1.IntroductionandMainResultLet(X,F)beaJBrXR'-valuedvector.AssumethatwhenX=xisgiven,thereexistsaconditionaldensityofYtobedenotedbyf(y[x),whichisaBorel-measurablefunctionof(x,y).Notethatwedonotassumetheexistenceofadensityfunctionof(X,F).Let(X-i,fi),—,(Xn,Fn)bei.i.d.samplesof(X,F).Ourpurposeistoestimatef(y\x)basedonthesesamples.Thisisaninterestingprobleminviewofeitherpuretheoryorpracticalapplications.MotivatedbytheideasuggestedinkernelandNNestimationsinthetheoryofnonparametricregressionanddensityestimates,thefirstauthorproposesthefollowingtwoclassesofestimatorsoff(y\x):
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简介:ForpartiallinearmodelY=X^Tβ0+go(T)+εwithunknownβ∈R^dandanunknownsmoothfunctiongo,thispaperconsiderstheHuber-Dutterestimatorsofβ0,scaleσfortheerrorsandthefunctiong0respectively,inwhichthesmoothingB-splinefunctionisused.Undersomeregularconditions,itisshownthattheHuber-Dutterestimatorsofβ0andσareasymptoticallynormalwithconvergenceraten^-1/2andtheB-splineHuber-Dutterestimatorofg0achievestheoptimalconvergencerateinnonparametricregression.AsimulationstudydemonstratesthattheHuber-Dutterestimatorofβ0iscompetitivewithitsM-estimatorwithoutscaleparameterandtheordinaryleastsquareestimator.Anexampleispresentedafterthesimulationstudy.
简介:Inthisarticle,apartiallylinearsingle-indexmodelforlongitudinaldataisinvestigated.Thegeneralizedpenalizedsplineleastsquaresestimatesoftheunknownparametersaresuggested.Allparameterscanbeestimatedsimultaneouslybytheproposedmethodwhilethefeatureoflongitudinaldataisconsidered.Theexistence,strongconsistencyandasymptoticnormalityoftheestimatorsareprovedundersuitableconditions.Asimulationstudyisconductedtoinvestigatethefinitesampleperformanceoftheproposedmethod.Ourapproachcanalsobeusedtostudythepuresingle-indexmodelforlongitudinaldata.
简介:剩余类型的一种新技术posteriori错误分析被开发因为低顺序的Raviart-Thomas混合了convection-diffusion-reaction方程的有限元素discretizations在二尺寸或三尺寸。集中的混合计划和迎风加权的混合计划被考虑。一个posteriori错误评估者,在L2标准加分级的排水量错误为压力变量错误发源,没有任何另外的费用,能直接与混合计划的答案被计算,并且被证明可靠。没有任何浸透假设,依赖于在系数的本地变化的本地效率被获得,并且从传送对流或反应不是到传送对流主导或反应主导的问题的现在的案例成立。分析的主要工具是修改奥斯瓦尔多插值的分级的排水量,抽象错误估计,和性质的postprocessed近似。数字实验被执行支持我们的理论结果并且显示出建议posteriori错误估计的竞争行为。[从作者抽象]