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All of Statistics A Concise Course in Statistical Inference - Wasserman.pdf

All of Statistics A Concise Cou…

lady 2011-01-22 评分 0 浏览量 0 0 0 0 暂无简介 简介 举报

简介:本文档为《All of Statistics A Concise Course in Statistical Inference - Wassermanpdf》,可适用于高等教育领域,主题内容包含PrefaceTakenliterally,thetitle“AllofStatistics”isanexaggerationButinspirit符等。

PrefaceTakenliterally,thetitle“AllofStatistics”isanexaggerationButinspirit,thetitleisapt,asthebookdoescoveramuchbroaderrangeoftopicsthanatypicalintroductorybookonmathematicalstatisticsThisbookisforpeoplewhowanttolearnprobabilityandstatisticsquicklyItissuitableforgraduateoradvancedundergraduatestudentsincomputerscience,mathematics,statistics,andrelateddisciplinesThebookincludesmoderntopicslikenonparametriccurveestimation,bootstrapping,andclassification,topicsthatareusuallyrelegatedtofollowupcoursesThereaderispresumedtoknowcalculusandalittlelinearalgebraNopreviousknowledgeofprobabilityandstatisticsisrequiredStatistics,datamining,andmachinelearningareallconcernedwithcollectingandanalyzingdataForsometime,statisticsresearchwasconductedinstatisticsdepartmentswhiledataminingandmachinelearningresearchwasconductedincomputersciencedepartmentsStatisticiansthoughtthatcomputerscientistswerereinventingthewheelComputerscientiststhoughtthatstatisticaltheorydidn’tapplytotheirproblemsThingsarechangingStatisticiansnowrecognizethatcomputerscientistsaremakingnovelcontributionswhilecomputerscientistsnowrecognizethegeneralityofstatisticaltheoryandmethodologyCleverdataminingalgorithmsaremorescalablethanstatisticianseverthoughtpossibleFormalstatisticaltheoryismorepervasivethancomputerscientistshadrealizedStudentswhoanalyzedata,orwhoaspiretodevelopnewmethodsforanalyzingdata,shouldbewellgroundedinbasicprobabilityandmathematicalstatisticsUsingfancytoolslikeneuralnets,boosting,andsupportvectorviiiPrefacemachineswithoutunderstandingbasicstatisticsislikedoingbrainsurgerybeforeknowinghowtouseabandaidButwherecanstudentslearnbasicprobabilityandstatisticsquicklyNowhereAtleast,thatwasmyconclusionwhenmycomputersciencecolleagueskeptaskingme:“WherecanIsendmystudentstogetagoodunderstandingofmodernstatisticsquickly”Thetypicalmathematicalstatisticscoursespendstoomuchtimeontediousanduninspiringtopics(countingmethods,twodimensionalintegrals,etc)attheexpenseofcoveringmodernconcepts(bootstrapping,curveestimation,graphicalmodels,etc)SoIsetouttoredesignourundergraduatehonorscourseonprobabilityandmathematicalstatisticsThisbookarosefromthatcourseHereisasummaryofthemainfeaturesofthisbookThebookissuitableforgraduatestudentsincomputerscienceandhonorsundergraduatesinmath,statistics,andcomputerscienceItisalsousefulforstudentsbeginninggraduateworkinstatisticswhoneedtofillintheirbackgroundonmathematicalstatisticsIcoveradvancedtopicsthataretraditionallynottaughtinafirstcourseForexample,nonparametricregression,bootstrapping,densityestimation,andgraphicalmodelsIhaveomittedtopicsinprobabilitythatdonotplayacentralroleinstatisticalinferenceForexample,countingmethodsarevirtuallyabsentWheneverpossible,IavoidtediouscalculationsinfavorofemphasizingconceptsIcovernonparametricinferencebeforeparametricinferenceIabandontheusual“FirstTerm=Probability”and“SecondTerm=Statistics”approachSomestudentsonlytakethefirsthalfanditwouldbeacrimeiftheydidnotseeanystatisticaltheoryFurthermore,probabilityismoreengagingwhenstudentscanseeitputtoworkinthecontextofstatisticsAnexceptionisthetopicofstochasticprocesseswhichisincludedinthelatermaterialThecoursemovesveryquicklyandcoversmuchmaterialMycolleaguesjokethatIcoverallofstatisticsinthiscourseandhencethetitleThecourseisdemandingbutIhaveworkedhardtomakethematerialasintuitiveaspossiblesothatthematerialisveryunderstandabledespitethefastpaceRigorandclarityarenotsynonymousIhavetriedtostrikeagoodbalanceToavoidgettingboggeddowninuninterestingtechnicaldetails,manyresultsarestatedwithoutproofThebibliographicreferencesattheendofeachchapterpointthestudenttoappropriatesourcesPrefaceixDatageneratingprocessObserveddataProbabilityInferenceandDataMiningFIGUREProbabilityandinferenceOnmywebsitearefileswithRcodewhichstudentscanusefordoingallthecomputingThewebsiteis:http:wwwstatcmuedularryallofstatisticsHowever,thebookisnottiedtoRandanycomputinglanguagecanbeusedPartIofthetextisconcernedwithprobabilitytheory,theformallanguageofuncertaintywhichisthebasisofstatisticalinferenceThebasicproblemthatwestudyinprobabilityis:Givenadatageneratingprocess,whatarethepropertiesoftheoutcomesPartIIisaboutstatisticalinferenceanditsclosecousins,dataminingandmachinelearningThebasicproblemofstatisticalinferenceistheinverseofprobability:Giventheoutcomes,whatcanwesayabouttheprocessthatgeneratedthedataTheseideasareillustratedinFigurePrediction,classification,clustering,andestimationareallspecialcasesofstatisticalinferenceDataanalysis,machinelearninganddataminingarevariousnamesgiventothepracticeofstatisticalinference,dependingonthecontextxPrefacePartIIIappliestheideasfromPartIItospecificproblemssuchasregression,graphicalmodels,causation,densityestimation,smoothing,classification,andsimulationPartIIIcontainsonemorechapteronprobabilitythatcoversstochasticprocessesincludingMarkovchainsIhavedrawnonotherbooksinmanyplacesMostchapterscontainasectioncalledBibliographicRemarkswhichservesbothtoacknowledgemydebttootherauthorsandtopointreaderstootherusefulreferencesIwouldespeciallyliketomentionthebooksbyDeGrootandSchervish()andGrimmettandStirzaker()fromwhichIadaptedmanyexamplesandexercisesAsonedevelopsabookoverseveralyearsitiseasytolosetrackofwherepresentationideasand,especially,homeworkproblemsoriginatedSomeImadeupSomeIrememberedfrommyeducationSomeIborrowedfromotherbooksIhopeIdonotoffendanyoneifIhaveusedaproblemfromtheirbookandfailedtogivepropercreditAsmycolleagueMarkSchervishwroteinhisbook(Schervish()),“theproblemsattheendsofeachchapterhavecomefrommanysourcesTheseproblems,inturn,camefromvarioussourcesunknowntomeIfIhaveusedaproblemwithoutgivingpropercredit,pleasetakeitasacompliment”IamindebtedtomanypeoplewithoutwhosehelpIcouldnothavewrittenthisbookFirstandforemost,themanystudentswhousedearlierversionsofthistextandprovidedmuchfeedbackInparticular,LizPratherandJenniferBakalreadthebookcarefullyRobReedervaliantlyreadthroughtheentirebookinexcruciatingdetailandgavemecountlesssuggestionsforimprovementsChrisGenovesedeservesspecialmentionHenotonlyprovidedhelpfulideasaboutintellectualcontent,butalsospentmany,manyhourswritingLATEXcodeforthebookThebestaspectsofthebook’slayoutareduetohishardworkanystylisticdeficienciesareduetomylackofexpertiseDavidHand,SamRoweis,andDavidScottreadthebookverycarefullyandmadenumeroussuggestionsthatgreatlyimprovedthebookJohnLaffertyandPeterSpirtesalsoprovidedhelpfulfeedbackJohnKimmelhasbeensupportiveandhelpfulthroughoutthewritingprocessFinally,mywifeIsabellaVerdinellihasbeenaninvaluablesourceoflove,support,andinspirationLarryWassermanPittsburgh,PennsylvaniaJulyPrefacexiStatisticsDataMiningDictionaryStatisticiansandcomputerscientistsoftenusedifferentlanguageforthesamethingHereisadictionarythatthereadermaywanttoreturntothroughoutthecourseStatisticsComputerScienceMeaningestimationlearningusingdatatoestimateanunknownquantityclassificationsupervisedlearningpredictingadiscreteYfromXclusteringunsupervisedlearningputtingdataintogroupsdatatrainingsample(X,Y),,(Xn,Yn)covariatesfeaturestheXi’sclassifierhypothesisamapfromcovariatestooutcomeshypothesissubsetofaparameterspaceΘconfidenceintervalintervalthatcontainsanunknownquantitywithgivenfrequencydirectedacyclicgraphBayesnetmultivariatedistributionwithgivenconditionalindependencerelationsBayesianinferenceBayesianinferencestatisticalmethodsforusingdatatoupdatebeliefsfrequentistinferencestatisticalmethodswithguaranteedfrequencybehaviorlargedeviationboundsPAClearninguniformboundsonprobabilityoferrorsContentsIProbabilityProbabilityIntroductionSampleSpacesandEventsProbabilityProbabilityonFiniteSampleSpacesIndependentEventsConditionalProbabilityBayes’TheoremBibliographicRemarksAppendixExercisesRandomVariablesIntroductionDistributionFunctionsandProbabilityFunctionsSomeImportantDiscreteRandomVariablesSomeImportantContinuousRandomVariablesBivariateDistributionsMarginalDistributionsIndependentRandomVariablesConditionalDistributionsxivContentsMultivariateDistributionsandiidSamplesTwoImportantMultivariateDistributionsTransformationsofRandomVariablesTransformationsofSeveralRandomVariablesAppendixExercisesExpectationExpectationofaRandomVariablePropertiesofExpectationsVarianceandCovarianceExpectationandVarianceofImportantRandomVariablesConditionalExpectationMomentGeneratingFunctionsAppendixExercisesInequalitiesProbabilityInequalitiesInequalitiesForExpectationsBibliographicRemarksAppendixExercisesConvergenceofRandomVariablesIntroductionTypesofConvergenceTheLawofLargeNumbersTheCentralLimitTheoremTheDeltaMethodBibliographicRemarksAppendixAlmostSureandLConvergenceProofoftheCentralLimitTheoremExercisesIIStatisticalInferenceModels,StatisticalInferenceandLearningIntroductionParametricandNonparametricModelsFundamentalConceptsinInferencePointEstimationConfidenceSetsContentsxvHypothesisTestingBibliographicRemarksAppendixExercisesEstimatingthecdfandStatisticalFunctionalsTheEmpiricalDistributionFunctionStatisticalFunctionalsBibliographicRemarksExercisesTheBootstrapSimulationBootstrapVarianceEstimationBootstrapConfidenceIntervalsBibliographicRemarksAppendixTheJackknifeJustificationForThePercentileIntervalExercisesParametricInferenceParameterofInterestTheMethodofMomentsMaximumLikelihoodPropertiesofMaximumLikelihoodEstimatorsConsistencyofMaximumLikelihoodEstimatorsEquivarianceofthemleAsymptoticNormalityOptimalityTheDeltaMethodMultiparameterModelsTheParametricBootstrapCheckingAssumptionsAppendixProofsSufficiencyExponentialFamiliesComputingMaximumLikelihoodEstimatesExercisesHypothesisTestingandpvaluesTheWaldTestpvaluesTheχDistributionxviContentsPearson’sχTestForMultinomialDataThePermutationTestTheLikelihoodRatioTestMultipleTestingGoodnessoffitTestsBibliographicRemarksAppendixTheNeymanPearsonLemmaThettestExercisesBayesianInferenceTheBayesianPhilosophyTheBayesianMethodFunctionsofParametersSimulationLargeSamplePropertiesofBayes’ProceduresFlatPriors,ImproperPriors,and“Noninformative”PriorsMultiparameterProblemsBayesianTestingStrengthsandWeaknessesofBayesianInferenceBibliographicRemarksAppendixExercisesStatisticalDecisionTheoryPreliminariesComparingRiskFunctionsBayesEstimatorsMinimaxRulesMaximumLikelihood,Minimax,andBayesAdmissibilityStein’sParadoxBibliographicRemarksExercisesIIIStatisticalModelsandMethodsLinearandLogisticRegressionSimpleLinearRegressionLeastSquaresandMaximumLikelihoodPropertiesoftheLeastSquaresEstimatorsPredictionMultipleRegressionContentsxviiModelSelectionLogisticRegressionBibliographicRemarksAppendixExercisesMultivariateModelsRandomVectorsEstimatingtheCorrelationMultivariateNormalMultinomialBibliographicRemarksAppendixExercisesInferenceAboutIndependenceTwoBinaryVariables