aspects of multivariate statistical theory 2ed（上）

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1、PrefaceThisbookhasgrownoutoflecturesgiveninfirst-andsecond-yeargraduatecoursesatYaleUniversityandtheUniversityofMichigan.Itisdesignedasatextforgraduatelevelcoursesinmultivariatestatisticalanalysis,andIhopethatitmayalsoprovetobeusefulasareferencebookforresearch

2、workersinterestedinthisarea.AnypersonwritingabookinmultivariateanalysisowesagreatdebttoT.W.Andersonforhis1958text,AnIntroduction10MultivariateStatisticalAnalysis,whichhasbecomeaclassicinthefield.Thisbooksynthesizedvarioussubareasforthefirsttimeinabroadoverview

3、ofthesubjectandhasinfluencedthedirectionofrecentandcurrentresearchintheoreticalmulti-variateanalysis.Itisalsolargelyresponsibleforthepopularityofmanyofthemultivariatetechniquesandproceduresincommonusetoday.ThecurrentworkbuildsonthefoundationlaidbyAndersonin195

4、8andinlargepartisintendedtodescribesomeofthedevelopmentsthathavetakenplacesincethen.OneofthemajordevelopmentshasbeentheintroductionofzonalpolynomialsandhypergeometricfunctionsofmatrixargumentbyA.T.JamesandA.G.Constantine.Toaverylargeextentthesehavemadepossible

5、aunifiedstudyofthenoncentraldistributionsthatariseinmultivariateanalysisunderthestandardassumptionsofnormalsampling.Thisworkisintendedtoprovideanintroductiontosomeofthistheory.Mostbooksofthisnaturereflecttheauthor’stastesandinterests,andthisisnoexception.Thema

6、infocusofthisworkisondistributiontheory,bothexactandasymptotic.Multivariatetechniquesdependheavilyonlatentrootsofrandommatrices;alloftheimportantlatentrootdistribu-tionsareintroducedandapproximationstothemarediscussed.Intestingproblemstheprimaryemphasishereiso

7、nlikelihoodratiotestsandthedistributionsoflikelihoodratioteststatistics,ThenoncentraldistributionsviiviiiPrejulteareneededtoevaluatepowerfunctions.Ofcourse,intheabsenceof“best”testssimplycomputingpowerfunctionsisoflittleinterest;whatisneededisacomparisonofpowe

8、rsofcompetingtestsoverawiderangeofalternatives.Whereverpossibletheresultsofsuchpowerstudiesintheliteraturearediscussed.IIshouldbementioned,however,thatalthoughtheemphasisisonlikeli