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1、TheoryofMultivariateStatisticsMartinBilodeauDavidBrennerSpringerAlam´emoiredemonp`ere,Arthur,`amam`ere,Annette,et`aKahina.M.BilodeauToRebeccaandDeena.D.BrennerThispageintentionallyleftblankPrefaceOurobjectinwritingthisbookistopresentthemainresultsofthemod-erntheoryofmultivariatestatisticstoanaudi
2、enceofadvancedstudentswhowouldappreciateaconciseandmathematicallyrigoroustreatmentofthatmaterial.Itisintendedforuseasatextbookbystudentstakingafirstgraduatecourseinthesubject,aswellasforthegeneralreferenceofinterestedresearchworkerswhowillfind,inareadableform,developmentsfromrecentlypublishedworkon
3、certainbroadtopicsnototherwiseeasilyaccessible,as,forinstance,robustinference(usingadjustedlikelihoodratiotests)andtheuseofthebootstrapinamultivariatesetting.Thereferencescontainsover150entriespost-1982.Themaindevelopmentofthetextissupplementedbyover135problems,mostofwhichareoriginalwiththeauthor
4、s.Aminimumbackgroundexpectedofthereaderwouldincludeatleasttwocoursesinmathematicalstatistics,andcertainlysomeexposuretothecalculusofseveralvariablestogetherwiththedescriptivegeometryoflinearalgebra.Ourbookis,nevertheless,inmostrespectsentirelyself-contained,althoughadefiniteneedforgenuinefluencying
5、eneralmathematicsshouldnotbeunderestimated.Thepaceisbriskanddemanding,requiringanin-tenselevelofactiveparticipationineverydiscussion.Theemphasisisonrigorousproofandderivation.Theinterestedreaderwouldprofitgreatly,ofcourse,frompreviousexposuretoawidevarietyofstatisticallymotivatingmaterialaswell,an
6、dasolidbackgroundinstatisticsattheundergraduatelevelwouldobviouslycontributeenormouslytoageneralsenseoffamil-iarityandprovidesomeextradegreeofcomfortindealingwiththekindsofchallengesanddifficultiestobefacedintherelativelyadvancedworkviiiPrefaceofthesortwithwhichourbookdeals.Inthisconnection,aspecifi
7、cintro-ductionofferingcomprehensiveoverviewsofthefundamentalmultivariatestructuresandtechniqueswouldbewelladvised.ThetextbookAFirstCourseinMultivariateStatisticsbyFlury(1997),publishedbySpringer-Verlag,providessuchbackg
