課程資訊

Advanced Statistical Inference (Ⅱ)

107-2

ECON5089

323 U1960

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1072ECON5089_

Contents:
1. Point Estimation: Review on UMVUE and MLE, Bayesian Point Estimation
3. Test of hypothesis.
4. Interval estimation.
5. Asymptotic methods
6. Topics of Linear model, generalized linear model and logistic model

The objective of this course is to introduce to the students of theory of inference including estimation, interval estimation and hypothesis testing. Both small and large sample theorems of hypothesis testing, interval estimation, and confidence intervals will cover. Applications to topics such as exponential families, linear models and nonparametric inference will be discussed.
It also provides a necessary basis for students for a further study of other advanced statistical courses.

Advanced statistical inference (I) or equivalent. Please refer to course webpage at ceiba.ntu.edu.tw on advanced Statistical Inference I (1001ASI)

Office Hours

Textbook and References:
1. Casella, G. and Berger, R. L. (2002). Statistical Inference. 2nd ed. Duxbury Press. (Textbook)
2. Rice, J.A. (1995). Mathematical Statistics and Data Analysis. 2nd edition. Duxbury Press.
3. Bickel, P. S. and Doksum, K. A. (2001). Mathematical Statistics: Basic Ideas and Selected Topics,
Vol. I, 2nd ed. Prentice Hall.
4. Lehmann, E. L. and Casella, G. (1998). Theory of Point Estimation. 2nd Edition, Springer.
5. Karr, A. F. (1993). Probability. Springer-Verlag.

(僅供參考)

 No. 項目 百分比 說明 1. Quizzes 20% two quizzes, Each is 10% of course grade. 2. Midterm 30% 3. Final 30% 4. Homeworks 20%

 課程進度
 週次 日期 單元主題 第1週 Review on UMVUE and method based on a sufficient and complete statistic. Point Estimation. Information bound and systematic procedure of finding UMVUE. (constrained optimization problem) 第2週 extreme value distributions and order statistics, probability inequality, method of mle with many parameters in Euclidean space, Bayesian point estimation and information integration 第3週 continuous 第4週 classical statistical inference: mle with finitely many parameters in Euclidean space 第5週 MLE: consistency and asymptotic normality under compactness parameter space, Bayes estimate (l1 and l2 penalties, lasso versus ridge), Bayes estimate 第6週 Quiz, MLE: consistency and asymptotic normality under compactness assumption (part 2) 第7週 Incomplete data: MCAR, MAR, Truncation; EM algorithm, Introduction of Bayes estimate, regularization. no class on 4/04 第8週 Monday: review; Thursday: midterm 第9週 自主學習週 第10週 Test of hypothesis: Framework, Neyman-Pearson lemma, Likelihood ratio test, 第11週 Wald test, and Score test (asymptotic distribution) , large sample test 第12週 Multi-normial distribution with large number of cells (Teaching model: histogram, kernel smoothing) 第13週 continue 第14週 Quiz 2 (5/20), Interval estimation and interpretation of confidence interval 第15週 GLM: generalized linear model and logistic regression model 第16週 Wrap up classical statistical estimation. 第17週 Topics: smoothing techniques for curve fitting 第18週 Monday: office hour, 期末考 final exam