基于ANOVA高维模型的正交设计的优良性.pdf

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1、应用概率统计第二十九卷ChineseJournalofAppliedProbability第六期2013年l2月andStatisticsVl01．29NO．6Dec．20l3OptimalPropertiesofOrthogonalArraysBasedonANOVAHigh-DimensionalModelRepresentationCHENXUEPING1,LINJINGUAN1WANGXIAODI3(DepartmentofMathematics，SoutheastUniversity，Nanjing，211189)(。DepartmentofMathematics，Jiangsu

2、UniversityofTechnology，Changzhou，213001)(。SchoolofSt。tistics，CentralUniversityofFinanceandEconomics，Beijing，100081)AbstractGlobalsensitivityindicesplayimportantrolesinglobalsensitivityanalysisbasedonANOVAhigh-dimensionalrepresentation，Wangetat．(2012)showedthatorthogonalarraysareA-optimalitydesigns

3、fortheestimationofparameter0M，thedefinitionofwhichcanbeseeninSection2．ThispaperpresentedseveralotheroptimalpropertiesoforthogonalarraysunderANOVAhigh．dimensionalrepresentation，includingE-optimalityfortheestimationofOManduniversalopti—malityfortheestimationof8M1where3MistheindependentparametersofOM

4、．Simulationstudyshowedthatrandomizedorthogonalarrayshavelessbiasedandmorepreciseinestimatingtheconfidenceintervalscomparingwithothermethods．Keywords：Matriximage，E-optimality,universaloptimality,orthogonalarray．AMSSubjectClassiflcation：62K05．§1．IntroductionTheANOVAhigh-dimensionalmodelrepresentatio

5、noriginatedfromHoefding(1948)，andwasfurtherdiscussedbyTakemura(1983)，EfronandStein(1981)andStein(1987)．ThatiSf(xi，⋯，m)=fo+∑fi(x~)+∑Aj(xi，J)+⋯+，12⋯m(1，⋯，xm)，Jwhere，0denotesthemeanefectwhichisaconstant．fi(xi)givestheefectofthevariablesXiindependentoftheotherinputvariables．(％xj)describestheinteractiv

6、eefectsofthevariablesXiandxj，andSOon．Model(1．1)hasseveralinterestingpropertiesundertheorthogonalcondition，／，{1．_屯(Xi1，⋯，Xi)dxk=0，fork=il，．．．，is．MoredetailscanbefoundinSobolf19931．TheprojectwassupportedbyNaturalScienceFoundationofJiangsuProvince(BK2011058)andNationalNaturalScienceFoundationofChina(

7、11171065and11301073)．ReceivedNovember9，2012．RevisedJuly23，2013．第六期陈雪平林金官王晓迪：基于ANOVA高维模型的正交设计的优良性571BasedonthisANOVAmodelrepresentation，Sobol(1993)proposedglobalsensitivityindex，1⋯=Dil_．．t。／D，where1．．．i。=var(1．．．i