作者	C.R.Rao/等
出版社
出版时间	1998-08-01

特色：

片断：Chapter5isdevotedtoestimationunderexactorstochasticlinearre-strictions.ThecomparisonoftwobiasedestimatorsaccordingtotheMDEcriterionisbasedonrecenttheoremsofmatrixtheory.Theresultsaretheoutcomeofintensiveinternationalresearchoverthelasttenyearsandap-pearhereforthefirsttimeinacoherentform.Thisconcernstheconceptoftheweakr-unbiasednessaswell.Chapter6containsthetheoryoftheoptimallinearpredictionandgives,inadditiontoknownresults,aninsightintorecentstudiesabouttheMDEmatrixcomparisonofoptimalandclassicalpredictionsaccordingtoalternativesuperioritycriteria.Chapter7presentsideasandproceduresforstudyingtheeffectofsingledatarowsontheestimationof.Here,differentmeasuresforrevealingoutliersorinfluentialpoints.includinggraphicalmethods,areincorporated.Someexamplesillustratethis.Chapter8dealswithmissingdatainthedesignmatrixX.Afterintroduc-ingthegeneralproblemsanddefiningthevariousmissingdatamechanismsaccordingtoRubin,wedemonstrate''adjustmentbyfollow-upinterviews"forlong-termstudieswithdropout.Fortheregressionmodelthemethodofimputationisdescribed,inadditiontotheanalysisofthelossofefficiencyincaseofareductiontothecompletelyobservedsubmodel.Themethodofweightedmixedestimatesispresentedforthefirsttimeinatextbookonlinearmodels.Chapter9containsrecentcontributionstorobuststatisticalinferencebasedonM-estimation.Chapter10describesthemodelextensionsforcategoricalresponseandexplanatoryvariables.Here.thebinaryresponseandtheloglinearmodelareofspecialinterest.Themodelchoiceisdemonstratedbymeansofexamples.Categoricalregressionisintegratedintothetheoryofgeneralizedlinearmodels.Anindependentchapter(AppendixA)onmatrixalgebrasummarizesstandardtheorems(includingproofs)thatareofinterestforthebookit-self,butalsoforlinearstatisticsingeneral.Ofspecialinterestarethetheoremsaboutdecompositionofmatrices(A.30-A.34),definitematrices(A.35-A.59),thegeneralizedinverse,andespeciallyaboutthedefinitenessofdifferencesbetweenmatrices(TheoremA.7l;cf.A.74-A.78).Thebookoffersanup-to-dateandcomprehensiveaccountofthetheoryandapplicationsoflinearmodels.TablesfortheX-and.F-distributionsareprovidedinAppendixB.2LinearModels2.1RegressionModelsinEconometricsThemethodologyofregressionanalysis,oneoftheclassicaltechniquesofmathematicalstatistics,isanessentialpartofthemoderneconometrictheory.Econometricscombineselementsofeconomics,mathematicaleconomics,andmathematicalstatistics.Thestatisticalmethodsusedineconometricsareorientedtowardspecificeconometricproblemsandhencearehighlyspecialized.Ineconomiclawsstochasticvariablesplayadistinctiverole.Henceeconometricmodels,adaptedtotheeconomicreality,havetobebuiltonappropriatehypothesesaboutdistributionpropertiesoftheran-domvariables.Thespecificationofsuchhypothesesisoneofthemaintasksofeconometricmodelling.Forthemodellingofaneconomic(orascientific)relation,weassumethatthisrelationhasarelativeconstancyoverasuffi-cientlylongperiodoftime(thatis,overasufficientlengthofobservationperiod),sinceotherwiseitsgeneralvaliditywouldnotbeascertainable.Wedistinguishbetweentwocharacteristicsofastructuralrelationship,thevariablesandtheparameters.Thevariables,whichwewillclassifylateron,arethosecharacteristicswhosevaluesintheobservationperiodcanvary.Thosecharacteristicsthatdonotvarycanberegardedasthestructureoftherelation.Thestructureconsistsofthefunctionalformoftherelation,includingtherelationbetweenthemainvariables,thetypeofprobabil-itydistributionoftherandomvariables,andtheparametersofthemodeiequations.