混合系数线性模型参数的有偏估计

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1、华北水利水电大学硕士学位论文II万方数据ABSTRACTANEWCLASSOFESTIMATIONFORCOEFFICIENTSINMIXED-EFFECTCOEFFICIENTLINEARMODELABSTRACTThelinearmodelisarichcontent,widelyapplicationbranchinmodernstatistics.Itisageneraltermforaclassofstatisticalmodel,whichuseamathematicalmodeltodeterminethelinearrelationshipbetweentheind

2、ependentvariablesandthedependentvariables.However,Inmanypracticalproblemsweoftenencounteredinamixed-effectcoefficientlinearmodel,namelythecoefficientsofthelinearmodelhasapartisfixed,andtheotherpartisrandom.Thismodeliswidelyusedineconomicanalysis,reliabilitydegradationanalysis,biological,medica

3、landotherfields,butthestructureandpropertiesofitisverydifferentformthegenerallinearmodel.Thispaperisbasedonthemixed-effectcoefficientlinearmodel,considerthemodelinthepresenceofmulticollinearity.Thebiasedestimateoftheparametersandexcellentpropertieswerediscussed.Themaincontentsareasfollows:(1)I

4、ntherepeated-measuresdatamodel,inordertodealwiththemulticollinearity,anew1*11*classofestimationdCMCICMZdfortheparametersinmixed-effectcoeff-icientlinearmodelisproposed.Undercertainconditions,thenewestimationareshowntobesuperiortotheGLSestimationandRidgeestimation,anddiscussitsadm

5、issibility,finallypresentsageneralizedformoftheestimation.(2)Forthemixed-effectcoefficientlinearmodel,intheconditionoftheexistenceofmulticollinearity,webasedonthetheoryofs-Kestimationandimproveit.Iftheeigenvalueislagerthanone,wecanstilluseLSestimation,anduses-Kestimationifitislessthanone.Anewc

6、lassofbiasedestimation:locals-Kestimationisproposed.Undercertainconditions,thenewestimationareshowntobesuperiortotheRidgeestimationandlocalSteinestimation.(3)Toimprovethes-Kestimation,wecanprovethegeneralizeds-KestimationarethelineartransformationofLSestimation,biasedestimationandcompressiones

7、timation.WhencomparedwithRidgeestimationandSteinestimation,theexcellentpropertiesoftheestimationwereproved.KEYWORDS:Biasedestimation；Leastsquaresestimation；LIUestimation；s-Kestimation；MeansquareerrorIII万方数据华北水利水电大学硕士学位论文IV万方数据目录目录摘要....