a goodness-of-fit test for bivariate extreme-value copulas

《a goodness-of-fit test for bivariate extreme-value copulas》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、Bernoulli17(1),2011,253275DOI:10.3150/10-BEJ279Agoodness-of-fittestforbivariateextreme-valuecopulasCHRISTIANGENEST1,IVANKOJADINOVIC2,JOHANNANELEHOVÁ3andJUNYAN41Départementdemathématiquesetdestatistique,UniversitéLaval,1045,avenuedelaMédecine,Québec,CanadaG1V0A6.E-mai

2、l:Christian.Genest@mat.ulaval.ca2Laboratoiredemathématiquesetapplications,UMRCNRS5142,UniversitédePauetdesPaysdelAdour,Boîtepostale1155,64013Paucedex,France.E-mail:Ivan.Kojadinovic@univ-pau.fr3DepartmentofMathematicsandStatistics,McGillUniversity,805,rueSherbrookeOu

3、est,Montréal(Québec),CanadaH3A2K6.E-mail:Johanna.Neslehova@math.mcgill.ca4DepartmentofStatistics,UniversityofConnecticut,215GlenbrookRoad,Storrs,CT06269,USA.E-mail:jun.yan@uconn.eduItisoftenreasonabletoassumethatthedependencestructureofabivariatecontinuousdistributi

4、onbelongstotheclassofextreme-valuecopulas.ThelatterarecharacterizedbytheirPickandsdependencefunction.Inthispaper,aprocedureisproposedfortestingwhetherthisfunctionbelongstoagivenparametricfam-ily.ThetestisbasedonaCramérvonMisesstatisticmeasuringthedistancebetweenanes

5、timateoftheparametricPickandsdependencefunctionandeitheroneoftwononparametricestimatorsthereofstudiedbyGenestandSegers[Ann.Statist.37(2009)29903022].Asthelimitingdistributionoftheteststatisticdependsonunknownparameters,itmustbeestimatedviaaparametricbootstrapprocedu

6、re,thevalidityofwhichisestablished.MonteCarlosimulationsareusedtoassessthepowerofthetestandanextensiontodependencestructuresthatareleft-taildecreasinginbothvariablesisconsidered.Keywords:extreme-valuecopula;goodnessoffit;parametricbootstrap;Pickandsdependencefunction

7、;rank-basedinference1.IntroductionLetXandYbecontinuousrandomvariableswithcumulativedistributionfunctionsFandG,respectively.FollowingSklar[36],thejointbehaviorofthepair(X,Y)canbecharacterizedatevery(x,y)∈R2bytherelationH(x,y)=Pr(X≤x,Y≤y)=C{F(x),G(y)}(1)throughaunique

8、copulaCthatcapturesthedependencebetweenXandY.WhenHisknown,itsmarginaldistributionscaneasilyberetrievedfromit.Thecopulacanalsobereadilyiden