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課程資訊

課程名稱

高等統計推論二
Advanced Statistical Inference (Ⅱ)

開課學期

100-2

授課對象

理學院數學研究所

授課教師

陳宏

課號

MATH7604

課程識別碼

221 U1580

班次

學分

全/半年

半年

必/選修

選修

上課時間

星期一4(11:20~12:10)星期四7,8(14:20~16:20)

上課地點

天數304天數304

備註

研究所統計科學組基礎課。
總人數上限：30人

Ceiba 課程網頁

http://ceiba.ntu.edu.tw/1002ASI

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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

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.

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)

預期每週課後學習時數

Office Hours

每週一 15:40~16:40
每週二 14:00~16:00
每週四 14:00~15:00
每週五 15:00~17:00 備註：週一、週四授課老師 (天文數學大樓465室) ; 週二2-4PM、週五3-5PM 助教 (天文數學館543室)

指定閱讀

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.

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	Homeworks	20%
2.	Midterm	30%
3.	Final	30%
4.	Quizzes	20%

課程進度

週次	日期	單元主題
第1週	02/20	Ch 6 Sufficiency, likelihood, and equivalence principles. General introduction of the course and data reduction through the concept of sufficient statistic.
第2週	2/27	03/03第三堂補週一的課，但授課老師於台中參加學術會議，暫定於03/05補課。 Ch6 Sufficiency, likelihood, and equivalence principles.
第3週	03/05	03/04停修申請開始, 03/03網路加選課程截止, Chapter 7: Point Estimation. Complete the systematic procedure of finding UMVUE.
第4週	03/12	週一上兩堂 (+1). Chapter 7: Point Estimation. Finish Theorem 6.2.13, define Ancillary Statistic and Present Basu's Theorem. Introduction of Bayes estimate.
第5週	03/19	週一上兩堂 (+2). (週四)第七堂Quiz 1，老師教統計通識課程. Chapter 7: Point Estimation; Finish Bayes Estimators and EM Algorithm. Quiz 1 tests your knowlege on the definition of sufficient statistic, minimal sufficient, finding UMVUE by using Rao-Blackwell theorem, Cramer-Rao lower bound.
第6週	03/26	週一上兩堂 (+2). (週四)第七堂不上課，老師教統計通識課程，第八堂上課。 Chapter 7: Point Estimation. EM algorithm and Loss Function of Optimality.
第7週	04/02	週一上兩堂 (+3)。4月2日上課，3-6日放假。 Chapter 8: Test of hypothesis: Setting of hypothesis testing, Neyman-Pearson paradigm
第8週	04/09	週一上兩堂(+3)，週四第七堂不上課，老師教統計通識課程，第八堂上課Chapter 8: Test of hypothesis
第9週	04/16	週一恢復上一堂，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	04/23	Chapter 8: Test of hypothesis; Chapter 10: Asymptotic methods
第11週	04/30	Chapter 10: Asymptotic methods: consistency and normality; bootstrap method
第12週	05/07	Chapter 10: bootstrap method, LR test, Wald test, and Score test (asymptotic distribution)
第13週	05/14	停修申請於5月18日止。 Chapter 9: Interval estimation; Chapter 10: Asymptotic methods: large sample test
第14週	05/21	週一 Quiz 2，週四不上課，授課老師赴美開會(+1)。
第15週	05/28	Chapter 10: Asymptotic methods, 周四未上課 (-1)
第16週	06/04	Optimal confidence interval and robustness, Intro Linear model 週一10:20-12:10 (0)
第17週	06/11	Monday: Quiz 6 on testing, confidence interval, and asymptotic analysis; Thursday: Topics of Linear model; generalized linear model and logistic model
第18週	06/18	週四: 期末考試。