海怨南曼王等大门餐 Parameter Estimation and Evaluation Professor Yongmiao Hong Cornell University April 21,2020
Parameter Estimation and Evaluation Professor Yongmiao Hong Cornell University April 21, 2020
CONTENTS 8.1 Population and Distribution Model 8.2 Maximum Likelihood Estimation 8.3 Asymptotic Properties of MLE 8.4 Method of Moments and Generalized Method of Moments 8.5 Asymptotic Properties of GMM 8.6 Mean Squared Error Criterion 8.7 Best Unbiased Estimators 8.8 Cramer-Rao Lower Bound 8.9 Conclusion Parameter Estimation and Evaluation Introduction to Statistics and Econometrics April 21,2020 2/207
Parameter Estimation and Evaluation Introduction to Statistics and Econometrics April 21, 2020 2/207 8.1 Population and Distribution Model 8.2 Maximum Likelihood Estimation 8.3 Asymptotic Properties of MLE 8.4 Method of Moments and Generalized Method of Moments 8.5 Asymptotic Properties of GMM 8.6 Mean Squared Error Criterion 8.7 Best Unbiased Estimators 8.8 Cramer-Rao Lower Bound 8.9 Conclusion CONTENTS
Parameter Estimation and Evaluation Population and Distribution Model Population and Distribution Model A random sample XT=(X1,..,Xn)is from a popula- tion distribution fx(x). A realization x"of the random sample Xm constitutes a data set with sample size n. [Sampling Inference:The primary purpose of sta- tistical inference is to make inference of the population distribution fx(x)using an observed data x". Population Inference Sampling 光光子状天 量元米米子 Sample Parameter Estimation and Evaluation Introduction to Statistics and Econometrics April 21,2020 3/207
Parameter Estimation and Evaluation Parameter Estimation and Evaluation Introduction to Statistics and Econometrics April 21, 2020 3/207 Population and Distribution Model Population and Distribution Model Sampling Inference
Parameter Estimation and Evaluation Population and Distribution Model Population and Distribution Model Parametric Approach]Consider a class of parametric candidate distributions F={f(,0):0∈Θ}， where f:2×O→R+is a known PMF/PDF function,2 is the support of Xi,is a parameter space that contains all plausible values for a p x 1 parameter vector 0,with p a fixed integer.Each value of 0e gives a distribution model for fx(x). Parameter Estimation and Evaluation Introduction to Statistics and Econometrics April 21,2020 4/207
Parameter Estimation and Evaluation Parameter Estimation and Evaluation Introduction to Statistics and Econometrics April 21, 2020 4/207 Population and Distribution Model Population and Distribution Model
Parameter Estimation and Evaluation Population and Distribution Model Population and Distribution Model Correct Model Specification:Assume that the class of functions F contains the population distribution fx(x) that generates the observed data.That is,there exists some unkonwn parameter value 00∈曰such that fx(c)=f(x,0o）for all a∈2. If F contains fx(),we call that the class of models F is correctly specified for the population distribution fx(), and 00 is called the true value of 0. Parameter Estimation and Evaluation Introduction to Statistics and Econometrics April 21,2020 5/207
Parameter Estimation and Evaluation Parameter Estimation and Evaluation Introduction to Statistics and Econometrics April 21, 2020 5/207 Population and Distribution Model Population and Distribution Model