Maximum Likelihood Estimation.pdf

《Maximum Likelihood Estimation.pdf》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、MaximumLikelihoodEstimationPhDEconometricsWeiTanHanqingAdvancedInstituteofEconomicsandFinanceRenminUniversityofChinaWeiTan(RUC)MaximumLikelihoodEstimation1/36MaximumLikelihoodEstimationIntroductionExamplesFrameworkforconditionalMLEConsistencyandAsymptoticPrope

2、rtyofMLEHypothesistestingWeiTan(RUC)MaximumLikelihoodEstimation2/36MaximumLikelihoodEstimationLinearModelscanbeestimatedwithoutmakingfulldistributionalassumptionsMainlyrelyonzerocovarianceandzeroconditionalmeanassummptions.EstimatesareconsistentWeiTan(RUC)Maxi

3、mumLikelihoodEstimation3/36MaximumLikelihoodEstimationAlternativeapproachistospecifythedistributionofrandomsampleMLEde…nesaclassofestimatorsbasedontheparticulardistributionassumedtohavegeneratedtheobservedrandomvariable.ThemainadvantageofMLestimatorsisthatamon

4、gallConsistentAsymptoticallyNormalEstimators,MLEshaveoptimalasymptoticproperties.Themaindisadvantageisthattheyarenotnecessarilyrobusttofailuresofthedistributionalassumptions.Theyareverydependentontheparticularassumptions.E¢ciencyvsRobustnessTradeo¤MLEprovidesa

5、uni…edapproachtoeconometricsanalysis,linearmodelscanbeviewedasatypeofMLEundercertainassumptions.WeiTan(RUC)MaximumLikelihoodEstimation4/36MaximumLikelihoodEstimationManynonlinearmodelscanbeestimatedbyMLEDiscreteResponseModels,suchasProbit,Logit,MultinomialLogi

6、t,OrderedProbitCensoredRegressionModel,suchasTobitCountDataModels,suchasPoissonandNegativeBinomialDurationModelWeiTan(RUC)MaximumLikelihoodEstimation5/36SetupoftheMLEThedistributionoftheobservedrandomvariableiswrittenasafunctionoftheparameterstobeestimated:P(y

7、ijdata;)=pdfjparametersThelikelihoodfunctionisconstructedfromtheparametricconditionaldensityfunction.Thedistributionofxisnotourinterest,weareonlyinterestedintheconditionaldistributionfunctionWeiTan(RUC)MaximumLikelihoodEstimation6/36probitSupposethatthelatentv

8、ariableyfollows:iy=x+eiiiwhereisavectorofparameters,eiisindependentofxiandei~Normal(0;1)Insteadofobservingthelatentvariabley,weobseverabinaryivariableyiand1ify>0y=ii0ify60i