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1、JournalofEconometrics168(2012)285–299ContentslistsavailableatSciVerseScienceDirectJournalofEconometricsjournalhomepage:www.elsevier.com/locate/jeconomRegularizationofnonparametricfrontierestimatorsAbdelaatiDaouiaa,b,∗,Jean-PierreFlorensa,LéopoldSimara,baToulouseSchoolofEconomics,France
2、bInstitutdeStatistique,UniversitéCatholiquedeLouvain,BelgiumarticleinfoabstractArticlehistory:Inproductiontheoryandefficiencyanalysis,weestimatetheproductionfrontier,thelocusofthemaximalReceived23September2009attainablelevelofanoutput(theproduction),givenasetofinputs(theproductionfacto
3、rs).Inothersetups,Receivedinrevisedformweestimateratheraninput(orcost)frontier,theminimalleveloftheinput(cost)attainableforagiven28October2011setofoutputs(goodsorservicesproduced).InbothcasestheproblemcanbeviewedasestimatingaAccepted19January2012surfaceundershapeconstraints(monotonicit
4、y,...).InthispaperwederivethetheoryofanestimatorofAvailableonline30January2012thefrontierhavinganasymptoticnormaldistribution.Itisbasedontheorder-mpartialfrontierwherewelettheordermtoconvergetoinfinitywhenn→∞butataslowrate.ThefinalestimatoristhencorrectedKeywords:foritsinherentbias.Wet
5、huscanviewourestimatorasaregularizedfrontier.Inaddition,theestimatorisProductionfunctionFreeDisposalHullmorerobusttoextremevaluesandoutliersthantheusualnonparametricfrontierestimators,likeFDHandNonparametricfrontierthantheunregularizedorder-mnestimatorofCazalsetal.(2002)convergingtothe
6、frontierwithaWeibullRobustestimationdistributionifmn→∞fastenoughwhenn→∞.TheperformancesofourestimatorsareevaluatedExtremevalueindexinfinitesamplesandcomparedtootherestimatorsthroughsomeMonte-Carloexperiments,showingabetterbehavior(intermsofrobustness,bias,MSEandachievedcoverageoftheres
7、ultingconfidenceintervals).Thepracticalimplementationandtherobustnesspropertiesareillustratedthroughsimulateddatasetsbutalsowitharealdataset.©2012ElsevierB.V.Allrightsreserved.1.Introductionproduced.Theattainableset(feasiblecombinationsofinputandoutputs)isdefinedasInproductiontheorya
