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ID:7322749
大小:12.51 MB
页数:400页
时间:2018-02-11
《aspects of multivariate statistical theory 2ed(上)》由会员上传分享,免费在线阅读,更多相关内容在工程资料-天天文库。
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
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