課程資訊

107-2

MATH7604

221 U1580

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1072MATH7604_infer

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

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.

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. 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