西南交通大学设备采购招标书_13178

ReviewofStatisticalInferencePreparedbyVeraTabakova,EastCarolinaUniversityC.1ASampleofDataC.2AnEconometricModelC.3EstimatingtheMeanofaPopulationC.4EstimatingthePopulationVarianceandOtherMomentsC.5IntervalEstimationSlideC-2PrinciplesofEconometrics,3rdEditionC.6HypothesisTestsAboutaPopulationMeanC.7SomeOtherUsefulTestsC.8IntroductiontoMaximumLikelihoodEstimationC.9AlgebraicSupplementsSlideC-3PrinciplesofEconometrics,3rdEditionSlideC-4PrinciplesofEconometrics,3rdEditionFigureC.1HistogramofHipSizesSlideC-5PrinciplesofEconometrics,3rdEditionSlideC-6PrinciplesofEconometrics,3rdEdition(C.1)[]EY(C.2)222var()[()][]YEYEYEYSlideC-7PrinciplesofEconometrics,3rdEdition(C.3)(C.4)iyyN1/NiiYYNSlideC-8PrinciplesofEconometrics,3rdEdition(C.3)(C.4)iyyN1/NiiYYNSlideC-9PrinciplesofEconometrics,3rdEditionSlideC-10PrinciplesofEconometrics,3rdEdition(C.5)1211111...NiNiYYYYYNNNNY1212111[]...111...111...NNEYEYEYEYNNNEYEYEYNNNNNNSlideC-11PrinciplesofEconometrics,3rdEdition(C.6)Y12122222222222111varvar...111=varvar...var111...NNYYYYNNNYYYNNNNNNNFigureC.2IncreasingSampleSizeandSamplingDistributionofSlideC-12PrinciplesofEconometrics,3rdEditionYYSlideC-13PrinciplesofEconometrics,3rdEditionCentralLimitTheorem:IfY1,…,YNareindependentandidenticallydistributed（i.i.d.）randomvariableswithmeanμandvarianceσ2,and,thenhasaprobabilitydistributionthatconvergestothestandardnormalN(0,1)asN./iYYNNYZNFigureC.3CentralLimitTheoremSlideC-14PrinciplesofEconometrics,3rdEditionSlideC-15PrinciplesofEconometrics,3rdEditionApowerfulfindingabouttheestimatorofthepopulationmeanisthatitisthebestofallpossibleestimatorsthatarebothlinearandunbiased(線性不偏).AlinearestimatorissimplyonethatisaweightedaverageoftheYi’s,suchas,wheretheaiareconstants.“Best”meansthatitisthelinearunbiasedestimatorwiththesmallestpossiblevariance.iiYaYSlideC-16PrinciplesofEconometrics,3rdEditionrrEY110EYEY2223344EYEYEYSlideC-17PrinciplesofEconometrics,3rdEdition(C.7)2222variYEYYYN22ˆ1iYYNSlideC-18PrinciplesofEconometrics,3rdEdition(C.9)(C.8)2ˆvarYNˆsevar/YYNInstatisticstheLawofLargeNumbers(大數法則)saysthatsamplemeansconvergetopopulationaverages(expectedvalues)asthesamplesizeN→∞.SlideC-19PrinciplesofEconometrics,3rdEditionrrEY2223344iiiYYNYYNYYNSlideC-20PrinciplesofEconometrics,3rdEdition3344skewnessSkurtosisKC.5.1IntervalEstimation:σ2KnownSlideC-21PrinciplesofEconometrics,3rdEdition(C.10)12~,NiiYYNYNN2~0,1YYZNNNPZzzFigureC.4CriticalValuesfortheN(0,1)DistributionSlideC-22PrinciplesofEconometrics,3rdEditionSlideC-23PrinciplesofEconometrics,3rdEdition(C.11)1.961.96.025PZPZ1.961.961.05.95PZ1.961.96.95PYNYNSlideC-24PrinciplesofEconometrics,3rdEdition(C.13)(C.12)1ccPYzYzNNcYzNWhenσ2isunknownitisnaturaltoreplaceitwithitsestimatorSlideC-25PrinciplesofEconometrics,3rdEdition(C.14)2ˆ.221ˆ1NiiYYN(1)ˆNYttNSlideC-26PrinciplesofEconometrics,3rdEdition(C.15)1ˆˆˆ1ccccYPttNPYtYtNNˆorseccYtYtYNSlideC-27PrinciplesofEconometrics,3rdEditionRemark:Theconfidenceinterval(C.15)isbasedupontheassumptionthatthepopulationisnormallydistributed,sothatisnormallydistributed.Ifthepopulationisnotnormal,thenweinvokethecentrallimittheorem,andsaythatisapproximatelynormalin“large”samples,whichfromFigureC.3youcanseemightbeasfewas30observations.Inthiscasewecanuse(C.15),recognizingthatthereisanapproximationerrorintroducedinsmallersamples.YYGivenarandomsampleofsizeN=50weestimatedthemeanU.S.hipwidthtobe=17.158inches.SlideC-28PrinciplesofEconometrics,3rdEdition2ˆˆ3.265therefore1.807ˆ1.80750.2556Nˆ1.80717.15822.0116.6447,17.671750cytNSlideC-29PrinciplesofEconometrics,3rdEditionComponentsofHypothesisTestsAnullhypothesis,H0(虛無假設)Analternativehypothesis,H1（對立假設）Ateststatistic（檢定統計量）Arejectionregion（拒絕域）Aconclusion（結論）TheNullHypothesis（虛無假設）The“null”hypothesis,whichisdenotedH0(H-naught),specifiesavaluecforaparameter.WewritethenullhypothesisasAnullhypothesisisthebeliefwewillmaintainuntilweareconvincedbythesampleevidencethatitisnottrue,inwhichcasewerejectthenullhypothesis.SlideC-30PrinciplesofEconometrics,3rdEdition0:.HcTheAlternativeHypothesis（對立假設）H1:μcIfwerejectthenullhypothesisthatμ=c,weacceptthealternativethatμisgreaterthanc.H1:μcIfwerejectthenullhypothesisthatμ=c,weacceptthealternativethatμislessthanc.H1:μ≠cIfwerejectthenullhypothesisthatμ=c,weacceptthealternativethatμtakesavalueotherthan(notequalto)c.SlideC-31PrinciplesofEconometrics,3rdEditionTheTestStatistic（檢定統計量）Ateststatistic’sprobabilitydistributioniscompletelyknownwhenthenullhypothesisistrue,andithassomeotherdistributionifthenullhypothesisisnottrue.SlideC-32PrinciplesofEconometrics,3rdEdition1~ˆNYttN(C.16)1~ˆNYcttN0If:istruethenHcSlideC-33PrinciplesofEconometrics,3rdEditionRemark:Thetests