課程資訊

105-2

MATH7604

221 U1580

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1052MATH7604_StatInf

Contents:
1. Sufficiency, likelihood, and equivalence principals.
2. 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% 2. Final 30% 3. Midterm 30% 4. Homeworks 20%

 課程進度
 週次 日期 單元主題 第1週 02/20, 02/23 Poisson RV (over dispersion), Large Sample theory, methods of estimation (MLE and Method of Moments). 第2週 02/18, 03/02 AR1 第3週 03/06, 03/09 03/06停修申請開始, 03/04網路加選課程截止, Chapter 7: Point Estimation. Complete the systematic procedure of finding UMVUE. 第4週 03/13, 03/16 Chapter 7: Point Estimation. Finish Theorem 6.2.13, define Ancillary Statistic and Present Basu's Theorem. Introduction of Bayes estimate. 第5週 03/20, 03/23 Chapter 7: Point Estimation 第6週 03/27, 03/30 Chapter 7: Point Estimation. EM algorithm and Loss Function of Optimality. 第7週 04/06 4月2-5日放假。 4月6日：Quiz 1 第8週 4/10, 4/13 Chapter 8: Test of hypothesis 第9週 4/17, 4/20 週四期中考。期中考範圍: 第6, 7章及第8章之8.1, 8.2.1, 8.2.2, 8.2.3(?), 8.3.1-8.3.4. 第10週 4/24, 4/27 Chapter 10: Asymptotic methods 第11週 5/01, 5/04 Chapter 10: Asymptotic methods: consistency and normality; bootstrap method 第12週 5/08, 5/11 Chapter 10: bootstrap method, LR test, Wald test, and Score test (asymptotic distribution) 第13週 5/15, 5/18 停修申請於5月19日止。 Chapter 9: Interval estimation; Chapter 10: Asymptotic methods: large sample test 第14週 5/22, 5/25 週一 Information Bound 第15週 6/01, 6/04 周四及週六上課: Likelihood ratio test, Information Bounds 第16週 6/05, 6/08 Optimal confidence interval and robustness, Intro Linear model 週一Quiz 3 11:20-12:10 第17週 6/12, 6/15 Monday: On testing, confidence interval, and asymptotic analysis; Thursday: Topics of Linear model; generalized linear model and logistic model 第18週 6/19 週四: 期末考試。