Intro to the Math. and Stat. Foundations of Econometrics - H. Bierens

《Intro to the Math. and Stat. Foundations of Econometrics - H. Bierens》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、1IntroductiontotheMathematicalandStatisticalFoundationsofEconometricsHermanJ.BierensPennsylvaniaStateUniversity,USA,andTilburgUniversity,theNetherlands2ContentsPrefaceChapter1:ProbabilityandMeasure1.1.TheTexaslotto1.1.1Introduction1.1.2Binomialnumbers1.1.3Samplespace1.1.4Algebrasandsigma

2、-algebrasofevents1.1.5Probabilitymeasure1.2.Qualitycontrol1.2.1Samplingwithoutreplacement1.2.2Qualitycontrolinpractice1.2.3Samplingwithreplacement1.2.4Limitsofthehypergeometricandbinomialprobabilities1.3.Whydoweneedsigma-algebrasofevents?1.4.Propertiesofalgebrasandsigma-algebras1.4.1Gene

3、ralproperties1.4.2Borelsets1.5.Propertiesofprobabilitymeasures1.6.Theuniformprobabilitymeasure1.6.1Introduction1.6.2Outermeasure1.7.LebesguemeasureandLebesgueintegral1.7.1Lebesguemeasure1.7.2Lebesgueintegral1.8.Randomvariablesandtheirdistributions31.8.1Randomvariablesandvectors1.8.2Distr

4、ibutionfunctions1.9.Densityfunctions1.10.Conditionalprobability,Bayes'rule,andindependence1.10.1Conditionalprobability1.10.2Bayes'rule1.10.3Independence1.11.ExercisesAppendices:1.A.CommonstructureoftheproofsofTheorems6and101.B.ExtensionofanoutermeasuretoaprobabilitymeasureChapter2:BorelM

5、easurability,Integration,andMathematicalExpectations2.1.Introduction2.2.Borelmeasurability2.3.IntegralsofBorelmeasurablefunctionswithrespecttoaprobabilitymeasure2.4.Generalmeasurability,andintegralsofrandomvariableswithrespecttoprobabilitymeasures2.5.Mathematicalexpectation2.6.Someuseful

6、inequalitiesinvolvingmathematicalexpectations2.6.1Chebishev'sinequality2.6.2Holder'sinequality2.6.3Liapounov'sinequality2.6.4Minkowski'sinequality2.6.5Jensen'sinequality2.7.Expectationsofproductsofindependentrandomvariables2.8.Momentgeneratingfunctionsandcharacteristicfunctions2.8.1Momen

7、tgeneratingfunctions42.8.2Characteristicfunctions2.9.ExercisesAppendix:2.A.UniquenessofcharacteristicfunctionsChapter3:ConditionalExpectations3.1.Introduction3.2.Propertiesofconditionalexpectations3.3.Conditionalprobabilitymeasuresandconditionalindependence3.4.Conditionin