统计学-数理统计在统计学中的地位（The position of statistical mathematical statistics in Statistics） 16页

统计学-数理统计在统计学中的地位（ThepositionofstatisticalmathematicalstatisticsinStatistics）I.Themaincharacteristicsofmathematicalstatisticsandstatistics(1)themainfeaturesofmathematicalstatistics;Themathematicalstatisticsisbasedontherandomphenomenonlimitedincomeobservationsorexperimentaldatasummarized,findrulesofthelimiteddata,andthenumberofrulesbasedonthecorrespondingoverallphenomenonmakeasubjectinferenceorjudgment.Summarizedasfollows:first,randomness,thatistosay,theobjectofmathematicalstatisticsshouldbestochastic,deterministicphenomenonisnotthecontentofmathematicalstatistics.Twoislimited,thatistosay,thenumberofrandomphenomenainmathematicalstatisticsislimitedbythenumberoftimes.Thethreeisquantitative,thatis,mathematicalstatisticstostudytherandomphenomenonofthenumberofregularitybased,andthequalityofrandomphenomenaforthesecondtime.Fouristheresearchmethodused,mainlyforinduction.Finally,mathematicalstatisticshasacertainprobabilityreliabilitythroughthestudyofsmallsamplesinordertoachievetheoverallinference.Thattheoverallerrorsampleisanobjectiveexistence,butstatisticsnotonlyfocusonthesizeoftheerror,theerrorpossibilityalsopointedout.Accordingtothecharacteristicsofmathematicalstatistics,mathematicalstatisticsisoneofthemostimportantandactivesubjectsinappliedmathematics.Thus!Statisticsfromthe\ndisciplinedivision,shouldbelongtomathematics,butitfocusesonapplication!Insteadofpuremathematicaltheoryormethodofresearch,themethodsusedarefocusingoninduction,ratherthanmathematicaldeduction.Insummary,themaincharacteristicsofmathematicalstatisticscanbesummarizedinonesentence,mathematicalstatisticsisalimitednumberofobservationsorexperimentsanumberofresearchresultsofrandomphenomena,accordingtothenumberofgeneralrulesmaketheappliedmathematicshascertainreliabilityinference.(two)themaincharacteristicsofStatisticsStatisticsisamethodologyscienceofcollecting,arrangingandanalyzingstatisticaldata.Thepurposeofstatisticsistoexploretheinternalquantityandregularityofdatasoastoachievescientificunderstandingofobjectivethings.Statisticsfromthescopeofitsresearch,therearethreemajorareas:datacollection,datacollationanddataanalysis.Firstofall,withthedevelopmentofstatistics,itisdifficulttotellwhichareasaremoreimportantinthesethreefields.Perhapsalotofpeoplethinkthatdataanalysisismoreimportant.IntheanalysisoftheUnitedStatesin1910and1900twoagriculturalcensusdata,Leninpointedout:"allproblems,allthedifficulttaskishowthesedatacanexactlyfromthepoliticalandeconomicsituationthatthedifferentkindsortypesoffarmers."Thisshowstheimportanceofdatacollation.Studyonanalysismethodofdistressstatisticsinourcountryisnotdatainrecentyears,butthelackofadequate\nstatisticaldatavalid,whichcannotbeconfirmedortotestthecorrespondingeconomictheory,economicmodelandeconomicpolicydata.Theimportanceofdatacollectionisevident.Second,statisticsisamethodologicalscience.Foralongtime,ithasbeenconsideredthatthebasicmethodsofstatisticalresearcharenumerousobservationmethod,statisticalindexmethod,statisticalgroupingmethodandmodelinferencemethod.Especiallyalotofobservationbecomesoneofthemostimportantbasiccharacteristicsofstatisticalmethods,itcanbesaidthatthisisoneofthefundamentaldifferencebetweenstatisticalandmathematicalstatisticsorstatisticsalsoreallyhasbecomethemodernWesternMathematicalStatistics.Withthestatisticsfromthepurelystatisticaldescriptionoftheearlydevelopmentforbothdescriptivestatisticsandinferentialstatistics,untilsomescholarsthinkthatthemodernstatisticsshouldbedominatedbystatisticalinference,supplementedbydescriptivestatistics,regardlessofwhethertheideainappropriate,butitcanbeinferredstatisticallyhasplayedanimportantroleinthemodernsociallife.Infact,inferentialstatisticshasbecomeoneofthebasicfeaturesofmodernstatistics.Again,thestatisticsfromonedaybecomeascience,thephenomenonofquantityresearchasthebasiccharacteristics,butalsotheirown,emphasizedtheneedforaqualitativeunderstandingofthephenomenonasthefoundation.(three)comparisonofmathematicalstatisticsandstatisticsThroughtheaboveanalysisofmathematicalstatisticsandstatisticalcharacteristics,themainsimilaritiesanddifferencesbetweenmathematicalstatisticsandstatisticscan\nbesummarizedasfollows:1.fromtheobjectivepointofview,bothfocusingonthenumberoflawrevealsthegeneralphenomenon,andwasclaimedtobemorequalitativetotheoverallunderstandingofthephenomenonasthefoundation.2.fromthewayofstudy,throughtheresearchonquantitativecharacteristicsoftheindividualpartofoverallhopeofmathematicalstatistics,inordertoachievetheoverallrecognitionofthecorrespondingnumberoffeatures;andbothstatisticsbyresearchingonquantitativecharacteristicsofthegeneralstructureofallindividuals(ifpossibleor$worthit),inordertoachievetheoverallunderstandingthecorrespondingnumberoffeatures,alsohopethatthroughtheresearchofquantitativecharacteristicsoftheindividualpartsoftheoverall,Inordertoachieveanunderstandingofthecorrespondingquantitativecharacteristicsofthepopulation.3.fromtheresearchmethods,thecorrespondingcharacteristicsofmathematicalstatisticsmainlydependsonthecharacteristicsofsmallsamplestatisticalmathematicsprincipletoinfertheoveralldistributionofvalue;andstatisticsorthecorrespondingcharacteristicsofstatisticalinferencemainlydependsontheeigenvaluesoflargesamplestatisticalmathematicsprincipletoinfertheoverallvaluedistribution.4.fromthemainscopeoftheirresearch,mathematical\nstatisticsfocusedonquantitativeanalysisofthesamplesandstatistics;notonlypaysattentiontothequantitativeanalysisofthesampledata,andattentionontheoverallanalysis,quantitativeobtainedallthedataatthesametime,theresearchmethodsofdatacollectionanddataprocessingmethod.5.fromthemathematicaldeductionoftheoveralluseofsampledata,theprobabilitytheoryisthecommonfoundation.Especiallyasoneofthebasicmethodsofstatisticalmethodofmassobservation,itsmathematicalbasisisthelawoflargenumbersinthetheoryofprobabilitystatistics;largesamplecanbeeasilyinferredfromthemathematicalbasisofgeneralcharacteristicsofitisthecentrallimittheoreminprobabilitytheory,andwhetheritisthelawoflargenumbersorthecentrallimittheoremisalsothefoundationofmathematicalstatistics.Althoughthe6.statisticsemphasizetheapplication,butitisamathematicaldiscipline,focusingontheapplicationofthemethodbasedonmathematicalstatistics;moreemphasisonresearchandapplicationofanalysismethodtosolvetheproblemofsocialeconomicandthenumberofscientificresearchandthemathematicalbasisofthemethoditself,bythetheoryofstatisticscorrespondingtoinfact,research,scientificresearchonthemathematicalbasisofstatisticalinferencemethod,isoneoftheresearchareasofmathematicalstatistics.Fromtheabovecharacteristicsandcomparisonofmathematicalstatisticsandstatistics,canseeclearlythatwiththe\ndevelopmentofmodernstatisticsandinthesocialpoliticalandeconomiclifeplayagrowingroleinthetrend,ideasandmethodstostudytheissueofmathematicalstatisticsonthedevelopmentofstatisticshasproducedrevolutionaryinfluence,butimportant,mathematicalstatisticsandstatisticsaretwosubjectsdifferent,cannotsimplybe"unified".Two,thestatusofmathematicalstatisticsinStatisticsStatisticsandstatisticsaretwodifferentdisciplines,theycannotreplaceeachother,cannotbelikeovertheyearssomescholarsproposedthat,toestablishastatisticalmatter,ortheintegrationofstatistics,itsessenceistocombinemathematicalstatisticsandstatistics.Butthedirectconsequencesoftheirfusionisnowusedbysomecollegesanduniversitiesinstatisticstextbooks,bothhavestatisticalcontent,therearestatisticalcomponents,weinfact,neitherfishnorfowl,simplesplicingcontentandcontentisthestatisticsofthestatistics.ThisisasadthingaboutChina'sstatistics,statisticstextbooksandstatisticalteachinginrecentyears:losingoneselfandblindlywantingtoconnectwiththewest".Theauthorbelievesthatinordertostraightenouttherelationshipbetweenmathematicalstatisticsandstatistics,itisnecessarytomakeathoroughstudyofthestatusofmathematicalstatisticsinstatistics.(1)thestatusofmathematicalstatisticsinthedevelopmentofstatisticalthinkingStatistics,asasocialpractice,hasahistoryofseveralthousandyears.Itispeople'ssimpleunderstandingof\nstatistics.Withthecontinuousdevelopmentofsocialproductivity,thecontemporarystatisticshasnotimprisonandplantotheunificationof"category.1.statisticsitisrecognizedasoneofthemostpowerfulweaponsofthesociety,hasbeenwidelyappliedinmanyfieldsofsociety,politics,economy,scienceandtechnology,andeachareahasitscomplexityanddiversity,thesimple"unification",namelyacomprehensivesurveyisalmostimpossible,butfullyunderstandtheregularityofcontactnumberthebasicsituationofeveryareaanddifferentareas,necessaryformodernsocialmanagement.Theideasandmethodsofmathematicalstatistics,naturallyforstatisticsbymathematicalstatistics,namelyforthedevelopmentofmodernstatisticslitasparkofscientificthoughttosolvecomplexproblems,aspartofthetotaltolaythefoundationofthemathematicaldescriptionofoverallThe2.20centurysince30s,withtheformationofthegovernmenttoeffectivelyintervenethenationaleconomicconcept,thegovernmentinthesocialeconomiclifeasadirectparticipant,theglobaldatabasedonthemaster,greatlypromotedthedevelopmentofstatisticalthinking,notonlyspendalotofmoneyonthestatistics"weapon"fordevelopment,ismoreimportantspecificationforstatisticalbehaviorfromtheangleoflegislation.Intoday'sstatisticallawsandregulationsofmanycountries,theimportanceofsamplingsurveyisclearlydefined.Forexample,inChinain19965menstrualchangesafterthepromulgationandimplementationofthe"People'sRepublicofChinastatisticallaw"secondchaptertenthclearlystipulates:"thestatisticalinvestigationshall\nbebasedonperiodicalcensuses,mainlythroughregularsamplingsurveys,bystatisticalreports,keyinvestigationandcomprehensiveanalysisassupplement,collection,finishingthebasicstatisticaldata".Thebasicprincipleofsamplingsurveyisbasedontheinferentialprincipleofmathematicalstatistics.Itcanbeseenthattheinferentialpositionofmathematicalstatisticsinstatisticalpracticehasbeenestablishedintheformoflaw.3.asthesocialeconomicactivitiesofthemainbusinessunits,inthebackgroundofthedevelopmentofworldeconomicglobalizationandregionaleconomicintegration,notonlydoesnothavesufficientfundsandtechnicalsupportinacomprehensiveinvestigation,sometimesnotnecessarythroughacomprehensivesurveytoobtaincomprehensivedataproductionbycamp,whichisenoughtoprovidethecorrespondingsamplesurveyreliabledataasthebasisofenterpriseproductionandmanagementdecision-making.Thisalsoshowsthatmathematicalstatisticshasmicrorealisticneeds,andopensupanunlimitedbroadprospectformicroeconomicmanagementactivities.Intheapplicationofmicrostatistics,thereisasolidideologicalfoundation.4.statisticalconcept,isnotonlythedescriptionofcharacteristicsofthedevelopmentofhistorywithhistoricaldata,andmoreemphasisoncontemporarythroughthecollectionandanalysisofhistoricaldata,topredictthefuture,basedonthispredictionisalsobasedontheprincipleofmathematicalstatistics.Thatistosay,tofindouttheinternalquantityandregularityofthedatafromthe\nhistoricaltimeseriesdata,soastograspthefuturetrend,thatis,thefunctionofthemathematicalstatisticsanalysisprincipleinthepredictionoftimeseriesdata,isequallyimportant.(two)thestatusofmathematicalstatisticsinstatisticalmethodsWiththeestablishmentoftheideaofsolvingrealisticproblemsinmathematicalstatistics,theimportanceofmathematicalstatisticsinstatisticalmethodshasbeencorrespondinglyestablished.Thelawofthe1.majornumberssetsupaconnectinglinkfortheapplicationofmathematicalstatisticsinstatistics.Largenumberofobservationisoneofthebasicmethodsofmodernstatistics,andthelawoflargenumbersisthefoundationofalargenumberofstatisticalobservationwithoutalargenumberofobservationsupport,thenstatisticalanalysisofthebasicindicators:theaveragenumberandrelativenumber,itlosesitsroleandsignificanceofthevisiblepositioninmathematicalstatisticsstatisticalmethodsallowalldoubt.The2.centrallimittheorempavesthewayfortheapplicationofmathematicalstatisticsinstatistics.Mastersampledistributionofeigenvaluesiskeytoinfertheoverallsample,andthecentrallimittheoremshowsthataslongasthesamplesizeissufficientlylargeand,sincethevalueoftheoverallcharacteristicsoftheunknownsampleapproximatenormaldistribution.Thus,aslongastheuseofalargenumberof\nobservationsobtainedrandomlyenoughsampledata,thestatisticscanbealmostalltreatmentmethodusedinstatistics,whichontheotherhandalsoindirectlyopenedupthefieldofstatisticalmethodanditsdominantpositioninthemodernstatisticalinferencemethodologyin.3.thetheoryofsamplingdistributioninmathematicalstatisticsprovidesthetheoreticalguaranteefortheapplicationofthemethodsofvarianceanalysisandorthogonaldesigninmodernstatistics.Inparticular,theroleoforthogonaldesigninthefieldofindustrialandagriculturalproductionanditscontributiontotheeconomyhaveattractedmuchattentionofforeignscholars.AccordingtosomeJapaneseexperts,"atleast10%ofJapan'seconomicdevelopmenthasbeenattributedtoorthogonaldesign."."Thisshowsthepracticalsignificanceofmathematicalstatisticsintheapplicationofstatisticalmethods.(three)thestatusofmathematicalstatisticsinstatisticalcontentStatisticsisamethodologicalscienceonhowtocollect,collateandanalyzestatisticaldata.Nomatterhowmuchimpactthedevelopmentofmathematicalstatisticsofstatisticalthoughts,regardlessofmathematicalstatisticsinthestatisticalmethodsinwhatposition,statusofmathematicalstatisticsinstatisticsismainlyreflectedinthestatisticalanalysisofthestatus.Theactualeffectofmathematicalstatisticsondatacollectionandcollationismuchlessthanthatofstatisticalanalysis.Thatistosay,statistics,asamethodologyscience,hasamuchlargerfieldofstudythan\nmathematicalstatistics.Trytoreplacethestatisticalviewpointwiththestatisticsclearlyisnotcorrect,alsotryingtoreplacethestatisticswithstatisticalpointofviewisnotcorrect,afterall,mathematicalstatisticsasamathematicaldisciplinehasitsownirreplaceablecharacteristics.Therefore,thestatusofmathematicalstatisticsinstatisticalcontentcanonlybemainlyreflectedinstatisticalanalysis.1.,theresearchofstatisticaldatacollectionmethodisstilloneofthemaincontentsofmodernstatistics.Asmentionedearlier,inourcountry,howtoobtainalargenumberofrealandeffectivestatisticaldataisoneoftheurgenttaskswearefacing.Untrueandincompletestatisticaldatacanmakethemacromanagementofthecountry"economictheory",theeconomicmodelandthestatisticaltestofeconomicpolicy,andtheproductionandoperationforecastanddecision-makingoftheenterprisecannotbeeffectivelycarriedout.Thus,thecorrectnessoftheviewthatthequalityofstatisticaldataisthelifeofallstatisticsiscorrect.Thestatisticsinthestatisticaldatacollectioneffectonlyreflectedinthestatisticaldatasurveymethods,samplingsurveymethodishowtoorganizetheimplementationoftheway,toemphasizethecollectionmethodinstatistics.2.samerawstatistics,Thecollationdataobtainedbydifferentfinishingmethodscanbecompletelydifferent,andthesamemethodcanbeusedtoanalyzethem.Theconclusionmaybecompletelyopposite.Thisisenoughtoillustratetheimportanceofstatistical\narrangement.However,mathematicalstatisticsisdifficulttoplayaneffectiveroleinstatisticalcollation.Afterall,themathematicalstatisticsresearchisbasedonsmallsamples,andstatisticalresearchisbasedonlargesamples.Ifstatisticsarenotbasedonalargesampleorpopulationofallindividuals,statisticsmayreallybereducedtomathematicalstatistics.3.theinfluenceofmathematicalstatisticsonstatisticaldataanalysisissignificant.Notonlyintheestimationofthelargesampleoverallparametersofnonparametricestimation,correlationandregressionanalysis,theoverallpatternofjudgment,ageneralparameterandtwooverallparameterhypothesistest,varianceanalysisandorthogonaldesignandmanyothercontent,butalsointhedescriptionofthemostbasicindicatorsinStatistics:averagenumberandrelativenumberthecalculationprinciple.Perhapsitisinconceivablethatinthecontentsystemofmodernstatisticalmethodsthereisalackofmathematicalstatisticsofthemethodsandprinciplesoflargesamples.Three,changetheconceptofstatisticalcommunicationThecharacteristicsofmathematicalstatisticsandstatisticsarestudied,andstatusofmathematicalstatisticsinthestatisticalanalyses,therealityletusreturntothedisseminationofknowledgeinstatistics,wecanseemoreclearlywhatI'mdoingnow,stillneedtobeimproved,inthefuturehowtodoabetterjobinwhathand.(1)thetransformationoftheconceptofstatisticalknowledgedisseminationismainlyembodiedinthefollowingthree\naspects:1.whatisstatistics?.Thisisthemostbasicunderstandingofstatistics,andcanbeachievedbystrengtheningthedisseminationofstatisticalknowledge.Inmodernstatisticalwork,although"unification"stillhasveryimportantpracticalsignificance,butinourstatisticalteachingandotherwaysofthedisseminationofstatisticalknowledge,mustnotbelimitedtothis.Notonlytomakepeopleofdifferentsocialclasses,tounderstandthestatisticsontheunderstandingoftheroleoftherealityofsociallife,andletthemknowthestatisticsinthenationalmacromanagement,businessforecasting,decision-making,andtheimportanceofeconomictheory#economicmodel,economicpolicytest,fromthestatisticalinvestigationthatallclassesofthepeople'sinitiativeparticipateinandcooperatewiththestatisticalagenciesatalllevelstocarryout,inordertoensurestatisticaldataintegrity.ThisrequiresthatChinashouldstrengthenstatisticalknowledge,universaleducationandpublicityandeducationofstatisticallawsandregulations,andopenupavarietyofwaysandmeansofstatisticalknowledgedissemination.Thisisthebasicconceptofstatisticalcommunication.2.,whydothedirectparticipantsinstatisticalactivitiesunderstandwhytheydoso?.Obviously,thisisahigherlevelofdemandforstatisticalcommunication.Knowingwhytodosoistoknowtheprincipleofstatistics,whichdoesnotrequireallcitizenstoknow.Infact,onlythosewhohaveacertainknowledgebasemayreallyunderstandthem,andtheirapproachesaremainlythroughstatisticalteachingactivitiesin\nInstitutionsofhigherlearning.Thisraisesthechallengeofteachingcollegestatistics:whatshouldstudentsteachinastatisticalclass?.TheauthorhasbeenengagedinStatisticsTeachingformanyyears,andbelievesthattheprinciplesofstatisticalmethodsshouldbeexplainedtostudentsinthestatisticsclass.Theclassroomteachingofstatisticsshouldnotbetoomuchemphasisonthestatisticalknowledgeofthepublicityandhowtoengageinstatisticalactivities,andshouldbepaymoreattentiontotheteachingofstatisticalmethodsthemechanismofdisseminationofideas,butintheteachingoftherealityofourcountryUniversitystatisticsandnotreallyformed.3.,howtodostatistics,whichisthespecificapplicationofstatisticalmethods.ItcanbesaidthattheteachingofstatisticsinChina'scollegesanduniversitiesisessentiallytoteachstudentshowtodopracticalstatisticalwork.Howtocollectandsortoutdata,howtouseformulastocalculatecertainindicators,etc..Itisobviousthatmiddleschoolstudentscandosuchwork.Andwhyisitnecessarytoorganizetheimplementationoftheinvestigationofthedata,collation,whydoyouwanttocalculate?.Notonlytheteacher'sintroductionisnotenough,butalsothedepthoftheteachingmaterialisnotenough.Thus,thedisseminationofstatisticalknowledgeshouldbebroadlydefinedonthreelevels:first,thedisseminationofbasicknowledgeofstatistics.Twoishowtocarryoutspecificstatisticalactivities.Three,whyisitpossibletocarryoutstatisticalactivitiesinsuchaway?.Therearedifferencesintheobjectsofcommunicationatdifferentlevels.Knowing\nwhatstatisticsis,howtodostatistics,andtherelativeunderstandingofwhyitshouldbedone,isverylow.Perhapsaslongasthenumberwillcount,willwritetheneighborhoodcommitteeaunt,youcanengageindatacollection,andwillapplytheformulaofasecondaryschoolstudentscancalculatetheX*2distributionofthestatisticsofthesamplevalue.Butknowingwhytodoso,withoutthecorrespondingmathematicalstatisticsknowledge,isabsolutelyimpossible.Ontheotherhand,withthepopularityofcomputersandthedevelopmentofstatisticaldataprocessingsoftware,Theuseofcomputerstoanalyzedatahasbecomeverysimple,andevenachildcanteachtheuseofstatisticalprocessingsoftware,inwhichcase.Isitimportantforstudentstoknowwhystatisticsdonotbecomeimportant?Onthecontrary,itismoreimportantforstudentstounderstandwhytheyareinacollegeclassroom.Four,thedirectionofthereformofstatisticaltextbooksinChinaFromthestatisticsofthespreadoftheconceptofdifferentlevelsofrequirements,knowledgestructureandmathematicalstatisticsinstatisticsandthestatusofthestudents,itisimperativetoreformthecurrentuniversitystatisticsteachingcontentsystemandteachingphilosophy.1.,removethecontentinthecurrentstatisticaltextbooksandmathematicalstatistics,andstrengthenthemathematicalstatisticscontentoflargesamples,thatis,toincreasethemathematicalbasisoflargesamplestatisticaldistribution.\n2.emphasizestheteachingofthelawsoflargenumbersandthecontentsofcentrallimittheorems.Althoughthesetwotheoremsarepurestatisticalproblems,butbecauseofitsmathematicalstatisticsteaching,teachersoftendonotpayenoughattention,becauseofthesmallsampleproblemisthemainproblem,themathematicalstatisticsandthereforemaybepassedover,andtheyjustisanimportantlinkofstatisticsandstatistics.Therefore,instatisticaltextbooks,thecontentmustbeincreasedandhighlighted.3.,increasethecontentofstatisticalmethodmechanism.Notonlyinthestatisticalinferencemechanismofstatisticalinferencemethods,butalsothemechanismofstatisticaldatacollectionmethodsandmethods.4.preparationofstatisticsteachingmaterialssuitableforspecificprofessionalneeds,inthepremiseofstrengtheningmechanismareintroducedvariousstatisticalmethods,combinedwithdifferentstudentsprofessionalpractice,introducesspecificapplicationofstatisticalmethodsinrelevantdisciplines,sothatallstudentsareabletotakethestatisticalmethodofquantitativeanalysisaccurately.Appliedtothepracticalworkinthefuture.