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1、Alam´emoiredemonp`ere,Arthur,`amam`ere,Annette,et`aKahina.M.BilodeauToRebeccaandDeena.D.BrennerPrefaceOurobjectinwritingthisbookistopresentthemainresultsofthemod-erntheoryofmultivariatestatisticstoanaudienceofadvancedstudentswhowouldappreciateaconciseandmathematicallyrig
2、oroustreatmentofthatmaterial.Itisintendedforuseasatextbookbystudentstakingafirstgraduatecourseinthesubject,aswellasforthegeneralreferenceofinterestedresearchworkerswhowillfind,inareadableform,developmentsfromrecentlypublishedworkoncertainbroadtopicsnototherwiseeasilyaccess
3、ible,as,forinstance,robustinference(usingadjustedlikelihoodratiotests)andtheuseofthebootstrapinamultivariatesetting.Thereferencescontainsover150entriespost-1982.Themaindevelopmentofthetextissupplementedbyover135problems,mostofwhichareoriginalwiththeauthors.Aminimumbackgr
4、oundexpectedofthereaderwouldincludeatleasttwocoursesinmathematicalstatistics,andcertainlysomeexposuretothecalculusofseveralvariablestogetherwiththedescriptivegeometryoflinearalgebra.Ourbookis,nevertheless,inmostrespectsentirelyself-contained,althoughadefiniteneedforgenuin
5、efluencyingeneralmathematicsshouldnotbeunderestimated.Thepaceisbriskanddemanding,requiringanin-tenselevelofactiveparticipationineverydiscussion.Theemphasisisonrigorousproofandderivation.Theinterestedreaderwouldprofitgreatly,ofcourse,frompreviousexposuretoawidevarietyofstat
6、isticallymotivatingmaterialaswell,andasolidbackgroundinstatisticsattheundergraduatelevelwouldobviouslycontributeenormouslytoageneralsenseoffamil-iarityandprovidesomeextradegreeofcomfortindealingwiththekindsofchallengesanddifficultiestobefacedintherelativelyadvancedworkviii
7、Prefaceofthesortwithwhichourbookdeals.Inthisconnection,aspecificintro-ductionofferingcomprehensiveoverviewsofthefundamentalmultivariatestructuresandtechniqueswouldbewelladvised.ThetextbookAFirstCourseinMultivariateStatisticsbyFlury(1997),publishedbySpringer-Verlag,provides
8、suchbackgroundinsightandgeneraldescriptionwithoutgettingmuchinvolvedinthe“nasty”detailsofanalysisandcon
