課程資訊
課程名稱
 高等統計推論二
Advanced Statistical Inference (Ⅱ) 
開課學期
 107-2 
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
 星期一5(12:20~13:10)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/1072MATH7604_infer 
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課程概述

Contents:
1. Point Estimation and probability inequalities: Review on UMVUE and MLE, Bayesian Point Estimation
2. Interval estimation and Test of hypothesis
3. Asymptotic methods: large sample theory
4. Topics of Linear model, generalized linear model and logistic model  

課程目標
 This course covers the fundamentals of theoretical statistics. The objective is to introduce students on the 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.
Topics include: , point and interval estimation, minimax theory, hypothesis testing, data reduction, convergence concepts, Bayesian inference, nonparametric statistics, bootstrap resampling, VC dimension, prediction and model selection. 
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 13:20~14:20
每週四 14:00~15:00 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 
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. 
 Final 
30% 
  
3. 
 Midterm 
30% 
  
4. 
 Quizzes 
20% 
 two quizzes, Each is 10% of course grade.  
 
課程進度
週次
日期
單元主題
第1週
 2/18, 21  UMVUE and method based on a sufficient and complete statistic. Point Estimation. Information bound and systematic procedure of finding UMVUE. (constrained optimization problem) Reference: http://theanalysisofdata.com/notes/RaoBlackwell.pdf 
第2週
 2/23, 25  Continue on UMVUE. Reference: http://pages.stat.wisc.edu/~doksum/STAT709/n709-29.pdf; http://pages.stat.wisc.edu/~doksum/STAT709/n709-30.pdf 
第3週
 3/04, 07  extreme value distributions and order statistics, probability inequality, method of mle with many parameters in Euclidean space, Bayesian point estimation and information integration Reference: http://www.math.ntu.edu.tw/~hchen/teaching/LargeSample/references/nagaraja.pdf 
第4週
 3/11, 14  classical statistical inference: mle with finitely many parameters in Euclidean space (compactness) and information bound. Refer to https://blogs.scientificamerican.com/roots-of-unity/what-does-compactness-really-mean/ 
第5週
 3/18, 21  MLE: consistency and asymptotic normality with unknown parameters fall into a compact space (Euclidean space), Bayes estimate (l1 and l2 penalties on unknown parameters, lasso versus ridge), Bayes estimate  
第6週
 3/25, 28  Quiz, MLE: consistency and asymptotic normality under compactness assumption (part 2) 
第7週
 4/01  Incomplete data: MCAR, MAR, Truncation; EM algorithm, Introduction of Bayes estimate, regularization. no class on 4/04 
第8週
 4/08, 11  MLE 
第9週
 4/15, 18  Review, midterm 
第10週
 4/22, 25  自主學習週 
第11週
 4/29, 5/02  Wald test, and Score test (asymptotic distribution) , large sample test  
第12週
 5/06, 13  Hypothesis Testing,  
第13週
 5/13, 16  bootstrapping 
第14週
 5/20, 23  GLM: generalized linear model and logistic regression model  
第15週
 5/27, 30  Topics: smoothing techniques for curve fitting 
第16週
 6/03, 06  asymptotic test 
第17週
 6/10, 13  Quiz on 6/10 
第18週
 6/17, 20  review, final test