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課程名稱 |
高等統計推論二
Advanced Statistical Inference (Ⅱ) |
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開課學期 |
105-2 |
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授課對象 |
理學院 應用數學科學研究所 |
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授課教師 |
陳 宏 |
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課號 |
MATH7604 |
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課程識別碼 |
221 U1580 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一4(11:20~12:10)星期四8,9(15:30~17:20) |
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上課地點 |
天數305天數305 |
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備註 |
研究所統計科學組基礎課。
限學士班三年級以上
總人數上限：35人
外系人數限制：15人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052MATH7604_StatInf |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
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
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課程目標 |
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. |
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課程要求 |
Advanced statistical inference (I) or equivalent. Please refer to course webpage at ceiba.ntu.edu.tw on advanced Statistical Inference I (1001ASI)
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預期每週課後學習時數 |
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Office Hours |
每週四 14:00~15:00
每週一 13:20~14:20 備註： 週一、週四 授課老師 (天文數學大樓465室) ; 週一1:20-2:20PM、週四14:00-15:00、週五3-5PM 助
教 (天文數學館543室) |
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指定閱讀 |
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參考書目 |
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.
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Quizzes |
20% |
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2. |
Final |
30% |
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3. |
Midterm |
30% |
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4. |
Homeworks |
20% |
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週次 |
日期 |
單元主題 |
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第1週 |
02/20, 02/23 |
Poisson RV (over dispersion), Large Sample theory, methods of estimation (MLE and Method of Moments). |
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第2週 |
02/18, 03/02 |
AR1
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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. |
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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. |
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第5週 |
03/20, 03/23 |
Chapter 7: Point Estimation |
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第6週 |
03/27, 03/30 |
Chapter 7: Point Estimation. EM algorithm and Loss Function of Optimality. |
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第7週 |
04/06 |
4月2-5日放假。 4月6日：Quiz 1 |
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第8週 |
4/10, 4/13 |
Chapter 8: Test of hypothesis |
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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. |
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第10週 |
4/24, 4/27 |
Chapter 10: Asymptotic methods |
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第11週 |
5/01, 5/04 |
Chapter 10: Asymptotic methods: consistency and normality; bootstrap method |
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第12週 |
5/08, 5/11 |
Chapter 10: bootstrap method, LR test, Wald test, and Score test (asymptotic distribution) |
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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 |
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第14週 |
5/22, 5/25 |
週一 Information Bound |
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第15週 |
6/01, 6/04 |
周四及週六上課: Likelihood ratio test, Information Bounds |
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第16週 |
6/05, 6/08 |
Optimal confidence interval and robustness, Intro Linear model 週一Quiz 3 11:20-12:10 |
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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 |
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第18週 |
6/19 |
週四: 期末考試。 |
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