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1、LectureNotesinStatistics184EditedbyP.Bickel,P.Diggle,S.Fienberg,U.Gather,I.Olkin,andS.ZegerViatcheslavB.MelasFunctionalApproachtoOptimalExperimentalDesignViatcheslavB.MelasMathematics&MechanicsFacultySt.PetersburgStateUniversity28,UniversityAvenue,Petrodvoretz198504St.Petersb
2、urg,Russiav.melas@pobox.spbu.ruLibraryofCongressControlNumber:2005930803ISBN-10:0-387-98741-XISBN-13:978-0387-98741-5Printedonacid-freepaper.©2006SpringerScience+BusinessMedia,Inc.Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionof
3、thepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnec-tionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmetho
4、dologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.
5、(MVY)987654321springeronline.comPrefaceThepresentbookisdevotedtostudyingoptimalexperimentaldesignsforawideclassoflinearandnonlinearregressionmodels.Thisclassincludespolynomial,trigonometrical,rational,andexponentialmodelsaswellasmanyparticularmodelsusedinecologyandmicrobiolog
6、y.Asthecriteriaofoptimality,thewellknownD-,E-,andc-criteriaareimplemented.Themainideaofthebookistostudythedependenceofoptimalde-signsonvaluesofunknownparametersandontheboundsofthedesigninterval.SuchastudycanbeperformedonthebaseoftheImplicitFunc-tionTheorem,theclassicalresulto
7、ffunctionalanalysis.Theideawasfirstintroducedintheauthor’spaper(Melas,1978)fornonlinearinparametersexponentialmodels.Recently,itwasdevelopedforothermodelsinanum-berofworks(Melas(1995,2000,2001,2004,2005),Dette,Melas(2002,2003),Dette,Melas,Pepelyshev(2002,2003,2004b),andDette,M
8、elas,Biederman(2002)).Thepurposeofthepresentbookistobringtogetherthe
