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1、MaximumLikelihoodEstimationofMisspecifiedModelsAuthor(s):HalbertWhiteReviewedwork(s):Source:Econometrica,Vol.50,No.1(Jan.,1982),pp.1-25Publishedby:TheEconometricSocietyStableURL:http://www.jstor.org/stable/1912526.Accessed:05/01/201321:17YouruseoftheJSTORarchiveindicatesyoura
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4、PMAllusesubjecttoJSTORTermsandConditionsECONOMETRICAICAVOLUME50JANUARY,1982NUMBER1MAXIMUMLIKELIHOODESTIMATIONOFMISSPECIFIEDMODELSBYHALBERTWHITE'Thispaperexaminestheconsequencesanddetectionofmodelmisspecificationwhenusingmaximumlikelihoodtechniquesforestimationandinference.The
5、quasi-maximumlikelihoodestimator(QMLE)convergestoawelldefinedlimit,andmayormaynotbeconsistentforparticularparametersofinterest.Standardtests(Wald,LagrangeMultiplier,orLikelihoodRatio)areinvalidinthepresenceofmisspecification,butmoregeneralstatisticsaregivenwhichallowinference
6、stobedrawnrobustly.ThepropertiesoftheQMLEandtheinformationmatrixareexploitedtoyieldseveralusefultestsformodelmisspecification.1.INTRODUCTIONSINCER.A.FISHERadvocatedthemethodofmaximumlikelihoodinhisinfluentialpapers[13,141,ithasbecomeoneofthemostimportanttoolsforestimationandi
7、nferenceavailabletostatisticians.Afundamentalassumptionunderlyingclassicalresultsonthepropertiesofthemaximumlikelihoodestima-tor(e.g.,Wald[32];LeCam[23])isthatthestochasticlawwhichdeterminesthebehaviorofthephenomenainvestigated(the"true"structure)isknowntoliewithinaspecifiedp
8、arametricfamilyofprobabilitydistributions(themodel).Inotherwords,the
