課程資訊
課程名稱
 高等統計推論二
Advanced Statistical Inference (Ⅱ) 
開課學期
 106-2 
授課對象
 理學院  應用數學科學研究所  
授課教師
 陳 宏 
課號
 MATH7604 
課程識別碼
 221 U1580 
班次
  
學分
 3.0 
全/半年
 半年 
必/選修
 選修 
上課時間
 星期一4(11:20~12:10)星期四8,9(15:30~17:20) 
上課地點
 天數305天數305 
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 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1062MATH7604_ 
課程簡介影片
 
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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) 
指定閱讀
 待補 
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
 2/26,3/01  bag of words model, one parameter exponential family 
第2週
 3/05,3/08  Probability Inequalities: Gaussian Tail Inequality, Hoeffding’s Inequality, Bounded Difference Inequality, maximum of random variables 
第3週
 3/12,3/15  MLE: consistency and asymptotic normality under compactness assumption (part 1) 
第4週
 3/19,3/22  MLE: consistency and asymptotic normality under compactness assumption (part 2) 
第5週
 3/26,3/29  probability inequality 
第6週
 4/02,4/05  probability inequality (cont.) 
第7週
 4/09,4/12  Introduction of Bayes estimate. EM algorithm (I) and Loss Function of Optimality.  
第8週
 4/16,4/19  Multinormial distribution with large number of cells (Teaching model: histogram), MLE under the assumption of compactness 
第9週
 4/23,4/26  4/23: Quiz 1; 4/26 midterm 
第10週
 4/30,5/03  No class! 自主學習週 
第11週
 5/07,5/10  Point Estimation. Information bound and systematic procedure of finding UMVUE.
Information Bound  
第12週
 5/14,5/17  Introduction of Bayes estimate. EM algorithm (I) and Loss Function of Optimality. Test of hypothesis: Framework, LR test, Wald test, and Score test (asymptotic distribution) , large sample test , Likelihood ratio test, 
第13週
 5/21,5/24  Test of hypothesis (cont.) 
第14週
 5/28,5/31  ToolBasedAsymptotic 
第15週
 6/04,6/07  Topics: generalized linear model and logistic model  
第16週
 6/11,6/14  Topics: smoothing techniques for curve fitting 
第17週
 6/18,6/21  6/18: no class; 6/21 wrap up Point 1:
What is Bayes estimate? Talk about prior and posterior link it with estimate with penalty such as ridge and lasso.
Point 2:
Bayes estimates are often can be written as a linear combination of mld and mode of prior.
References for Bayes estimate
https://newonlinecourses.science.psu.edu/stat414/node/241/