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1、AmericanSocietyforQualityGeneralizedCross-ValidationasaMethodforChoosingaGoodRidgeParameterAuthor(s):GeneH.Golub,MichaelHeathandGraceWahbaSource:Technometrics,Vol.21,No.2(May,1979),pp.215-223Publishedby:AmericanStatisticalAssociationandAmericanSocietyforQualityStableURL:http://www.jstor.org/stabl
2、e/1268518.Accessed:16/05/201307:52YouruseoftheJSTORarchiveindicatesyouracceptanceoftheTerms&ConditionsofUse,availableat.http://www.jstor.org/page/info/about/policies/terms.jsp.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrus
3、teddigitalarchive.Weuseinformationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org..AmericanStatisticalAssociationandAmericanSocietyforQualityarecollaboratingwithJSTORtodigitize,preserveandextendaccesstoTechnome
4、trics.http://www.jstor.orgThiscontentdownloadedfrom158.182.168.57onThu,16May201307:52:14AMAllusesubjecttoJSTORTermsandConditionsTECHNOMETRICS?,VOL.21,NO.2,MAY1979GeneralizedCross-ValidationasaMethodforChoosingaGoodRidgeParameterGeneH.GolubMichaelHeathDepartmentofComputerScienceComputerSciencesDiv
5、isionStanfordUniversityOakRidgeNationalLaboratoryStanford,CA94303OakRidge,TN37830GraceWahbaDepartmentofStatisticsUniversityofWisconsinMadison,WI53705Considertheridgeestimate:(A)for3inthemodely=Xf+E,e~3(0,a21),a2unknown,0(X)=(XTX+nXI)-XTy.Westudythemethodofgeneralizedcross-validation(GCV)forchoosi
6、ngagoodvalueXforX,fromthedata.TheestimateXistheminimizerofV(A)givenby-V({)-
7、I(-A(X))y2/Trace(A(X)),whereA(X)=X(X7X+nXI)-'X.Thisestimateisarotation-invariantversionofAllen'sPRESS,orordinarycross-validation.Thisestimatebehaveslikeariskimprovementestimator,butdoesnotrequireanestimateofa2,socanbeuse
8、dwhenn-pissmall,orevenifp>nincertaincases.TheGCVmethodcanalsobeusedinsubsetselectionandsingularvaluetruncationmethodsforregression,andeventochoosefromamongmixturesofthesemethods.KEYWORDS=(XTX)-1XTy.(SeeBerger[8],Thiste
