課程資訊

106-2

MATH7604

221 U1580

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1062MATH7604_

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. 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/