正交表的數據分析及其構造.pdf

1、2006屆研究生博士學位論文y896486學校代碼：10269學號：“YB03124002霉黧鐔赫震學正交表的數據分析及其構造院系：蕉讓丞專業(yè)：煎空迨生數堡統讓研究方向：試驗邀過指導教師：蘊壹松救援博士研究生：韭虐出2006年4月完成AbstractTherearethreepiecesofwritingwhichincludetenchaptersinthispaperInthefirstpieceofwriting，anewmeth

2、odofdataanalysisoforthogonalarraysfromglobaltolocalisproposed，calledGLAlgorithm(GlobalLocalAlgorithm)，whichgivesUSawaytofindoutastablecenterofaknownorunknownmultivariatefunctionThestablecenterisarowvectorwithentriesfromr

3、ealfieldThereisamultivariatefunctionsuch出atitsvalueontherowvectoristoagiventargetanditsfluctuationonagivenmulti—intervalsistobeminimizedInthesecondpieceofwriting，anewconstructingmethodoforthogonalarraysbyorthogohaldecomp

4、ositionsofprojectionmatricesisproposed，calledMIconstruction(MatrixImageConstruction)，whichgivesusawaytoconstructalotoforthogonalarraysusedinGLAlgorithmThematriximage如ofthejthcolumninallorthogonalarrayisaprojecdonmatrixco

5、rrespondingto髯=Yr山Y，thesumofsquaresofthejthfactorintheanalysisofvailaliceTheindependenceofthesunlsofsquares印and霹isequivalenttotheorthogonalityofmatriximagesAiand4，whiletheorthogonalityofmatriximagesAand^isequivalenttotha

6、toforthogonuiarraysThusthedataanalysisofadesigncannotonlybeobtainedbyorthogonaldecompositionsofprojectionmatrices，butalsoorthogonalarrayscanbeobtainedbyorthogonaldecompositionsofprojectionmatricesThemethodsofconstructing

7、orthogonalarraysinhistoryusuallyobtainedafewofsymmetryorthogonalarraysbuttheMIconstructioncanobtainedanumberofmixed1evelonesInthethreepieceofwriting，alotofapplicationtechnologyofGLAlgorithm，suchasindextransformation，prob

8、lemtransformationanddatatransformation，havebeengivenTheindextransformationimpliesanumberofmathematicalindiescanbetransformedintothoseofGLAlgorithmTheproblemtransformationimpliesanumberofstatisticalproblemscanbealsotransf

9、ormedintothoseofGLAlgorithmThedatatransformationimpliesanumberofdatafromthenonorthogonaldesignscanbealsotransformedintothedataunderorthogonaldesignsofGLAlgorithmAllinall，theGLAlgorithmhaseveryreasontobebelievedasanoperat