人民大学高级计量经济学讲义6

Econometric Theory,Lecturer: Dr.Jingtao Yi Room 715 Business School, RUC,Lecture 6: k-Variable Linear Regression IV,1. Asymptotic Theory;2. Asymptotic Properties of the OLS Estimator.,渐进分析，当从小样本扩大到大样本以后，X可能从非随机变为随机，因此求期望无法穿透，意味着估计量可能不是无偏的。为了解决问题，引入问题：概率的渐进和分布的渐进。渐进有效性。,Asymptotic Theory,Convergence in ProbabilityConvergence in Distribution,Convergence in Probability,Convergence in Probability,Convergence in Probability,Khinchines Weak Law of Large Numbers,Convergence in Distribution,Convergence in Distribution,Central Limit Theorem,Lindberg-Levy Central Limit Theorem (Univariate),Central Limit Theorem,Lindberg-Levy Central Limit Theorem (Multivariate),Asymptotic Properties of the OLS Estimator,Asymptotic Properties of the OLS Estimator: large-sample properties Consistency Asymptotic Normality Asymptotic Efficiency,Consistency,Consistency,Consistency,方差分解。模型的方差=模型可以解释的方差var(e)+模型解释的方差var(yhat),期望分解。模型的期望,Asymptotic Normality,Asymptotic Normality,Consistency of Covariance Matrix of b,Asymptotic Efficiency,An estimator is asymptotically efficient if it is consistent, asymptotically normally distributed, and has an asymptotic covariance matrix that is not larger than the asymptotic covariance matrix of any other consistent, asymptotically normally distributed estimator.,Asymptotic Efficiency,