chapter5 - Multiple Regression Analysis---Asymptotic Properties(1&amp#215;4).pdf

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1、2015/10/19ChapterOutline本章大纲MultipleRegressionAnalysisAsymptoticPropertiesSamplingDistribution样本分布Consistency一致性LargeSampleInferenceandAsymptoticy=0+1x1+2x2+...Normality大样本推断和渐近正态分布kxk+uAsymptoticEfficiency渐近有效性12SamplingDistribution样本分布(1)Samp

2、lingdistributionsplayacentralroleinthedevelopmentofstatisticalandeconometricprocedures.样本分布在统计学和计量经济学发展中具有核心地位Itistheprobabilitydistributionofanestimatoroverallpossibleoutcomes.SAMPLINGDISTRIBUTION它是指一个估计量在其所有可能取值上的概率分布渐近分布Therearetwoapproacheschara

3、cteringsamplingdistributions:an“exact”approachandan“approximate”approach.有两种描述样本分布的方法，一是“精确”的方法，一是“近似”方法。The“exact”approachhadbediscussedinthepreviouschapter.“精确”方法在前面章节已经介绍，本章主要介绍“近似”方法。3412015/10/19SamplingDistributionTheLawofLargeNumbers样本分布(2)大数定

4、律The“approximate”approachusesapproximationstothesamplingdistributionsthatrelyonthesamplesizebeinglarge.Thelawsaysthatundergeneralconditions,thesampleaveragewillbeclosetothepopulationmeanwithveryhighprobability“近似”方式依靠大样本，对样本分布进行近似描述。whenthesamplesize

5、islarge.Thelargesampleapproximationtothesamplingdistributionisoftencalledtheasymptoticdistribution.大数定律：在一般情形下，当样本量充分大时，样本均值对样本分布的大样本近似常称为渐近分布。将以很大的概率（接近1的概率）逼近总体均值。Theasymptoticdistributionscanbecountedontoprovidedgoodapproximationstotheexactsampli

6、ngdistribution,aslongasthesampleTheconditionsforthelawoflargenumberthatwewilluseinsizeislarge.thiscoursearethatyarei.i.drandomdrawsandtheits只要样本量足够大，渐近分布就是对准确分布的很好的近varianceisfinite似。本课中，为了应用大数定律，我们假设y为独立同分布且具Twokeytools:thelawoflargenumbers,andthec

7、entrallimittheorem.有有限方差的随机样本。两个重要工具：大数定律，中心极限定理。56TheCentralLimitTheorem中心极限定理22Supposethaty,y,...,yarei.i.dwithmeanandvariance,where0.12nyy2Asny,thedistributionof()/becomearbitrarilywellapproximatedbyythestandardnormaldistribution.如果y,y,..

8、.,y22012ny来自均值为方差为（y）的独立同分布CONSISTENCYy的随机样本，当n时，的分布和标准正态分布任意接近！2y一致性Thistheoremstatesthatundergeneralconditions,thesamplingdistributionofthestandardizedsampleaverageiswellapproximatedbyastandardnormaldistributionwhen