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1、c12-RobustEstimationPage407Thursday,October26,20062:10PMCHAPTER12RobustEstimationnthischapterwediscussmethodsforrobustestimation,withparticu-Ilaremphasisontherobustestimationofregressions.Robustestima-tionisatopicofrobuststatistics.Thereforewefirstintroduce
2、thegeneralconceptsandmethodsofrobuststatisticsandthenapplythemtoregressionanalysis.Inparticular,wewillintroducerobustregressionestimatorsandrobustregressiondiagnostics.ROBUSTSTATISTICSRobuststatisticsaddressestheproblemofmakingestimatesthatareinsensitiveto
3、smallchangesinthebasicassumptionsofthestatisticalmodelsemployed.Theconceptsandmethodsofrobuststatisticsorigi-natedinthe1950s.Thetechnicalterm“robuststatistics”wascoinedbyG.E.P.Boxin1953.However,theconceptsofrobuststatisticshadbeenusedmuchearlier,forexample
4、bythephysicistArthurEddingtonandthegeophysicistHaroldJeffreys.Statisticalmodelsarebasedonasetofassumptions;themostimportantinclude(1)thedistributionofkeyvariables,forexamplethenormaldistributionoferrors,and(2)themodelspecification,forexam-plemodellinearityo
5、rnonlinearity.Someoftheseassumptionsarecriti-caltotheestimationprocess:iftheyareviolated,theestimatesbecomeunreliable.Robuststatistics(1)assessesthechangesinestimatesduetosmallchangesinthebasicassumptionsand(2)createsnewestimatesthatareinsensitivetosmallch
6、angesinsomeoftheassumptions.Thefocusofourexpositionistomakeestimatesrobusttosmallchangesinthedistributionoferrorsand,inparticular,tothepresenceofoutliers.Robuststatisticsisalsousefultoseparatethecontributionofthetailsfromthecontributionofthebodyofthedata.W
7、ecansaythat407c12-RobustEstimationPage408Thursday,October26,20062:10PM408FINANCIALECONOMETRICSrobuststatisticsandclassicalnonrobuststatisticsarecomplementary.Byconductingarobustanalysis,onecanbetterarticulateimportanteconometricfindings.Wewillseelaterexampl
8、esofhowrobuststatisticsshedsnewlightonanumberofwell-knownempiricalfindings.1AsobservedbyPeterHuber,robust,distribution-free,andnonpara-metricalseemtobecloselyrelatedpropertiesbutactuallyarenot.2Forexample,thes
