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Course title |
高等統計推論二
Advanced Statistical Inference (Ⅱ) |
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Semester |
106-2 |
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Designated for |
COLLEGE OF SCIENCE Institute of Applied Mathematical Sciences |
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Instructor |
陳 宏 |
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Curriculum Number |
MATH7604 |
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Curriculum Identity Number |
221 U1580 |
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Class |
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Credits |
3.0 |
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Full/Half
Yr. |
Half |
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Required/
Elective |
Elective |
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Time |
Monday 4(11:20~12:10) Thursday 8,9(15:30~17:20) |
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Room |
天數305天數305 |
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Remarks |
研究所統計科學組基礎課。
Restriction: juniors and beyond
The upper limit of the number of students: 35.
The upper limit of the number of non-majors: 15. |
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Ceiba Web Server |
http://ceiba.ntu.edu.tw/1062MATH7604_ |
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Course introduction video |
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Table of Core Capabilities and Curriculum Planning |
Table of Core Capabilities and Curriculum Planning |
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Course Syllabus
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Please respect the intellectual property rights of others and do not copy any of the course information without permission
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Course Description |
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
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Course Objective |
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. |
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Course Requirement |
Advanced statistical inference (I) or equivalent. Please refer to course webpage at ceiba.ntu.edu.tw on advanced Statistical Inference I (1001ASI)
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Student Workload (expected study time outside of class per week) |
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Office Hours |
Thu. 14:00~15:00
Mon. 13:20~14:20 Note: 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) |
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Designated reading |
待補 |
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References |
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.
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Grading |
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No. |
Item |
% |
Explanations for the conditions |
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1. |
Homeworks |
20% |
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2. |
Midterm |
30% |
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3. |
Final |
30% |
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4. |
Quizzes |
20% |
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Week |
Date |
Topic |
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第1週 |
2/26,3/01 |
bag of words model, one parameter exponential family |
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第2週 |
3/05,3/08 |
Probability Inequalities: Gaussian Tail Inequality, Hoeffding’s Inequality, Bounded Difference Inequality, maximum of random variables |
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第3週 |
3/12,3/15 |
MLE: consistency and asymptotic normality under compactness assumption (part 1) |
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第4週 |
3/19,3/22 |
MLE: consistency and asymptotic normality under compactness assumption (part 2) |
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第5週 |
3/26,3/29 |
probability inequality |
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第6週 |
4/02,4/05 |
probability inequality (cont.) |
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第7週 |
4/09,4/12 |
Introduction of Bayes estimate. EM algorithm (I) and Loss Function of Optimality. |
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第8週 |
4/16,4/19 |
Multinormial distribution with large number of cells (Teaching model: histogram), MLE under the assumption of compactness |
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第9週 |
4/23,4/26 |
4/23: Quiz 1; 4/26 midterm |
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第10週 |
4/30,5/03 |
No class! 自主學習週 |
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第11週 |
5/07,5/10 |
Point Estimation. Information bound and systematic procedure of finding UMVUE.
Information Bound |
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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, |
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第13週 |
5/21,5/24 |
Test of hypothesis (cont.) |
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第14週 |
5/28,5/31 |
ToolBasedAsymptotic |
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第15週 |
6/04,6/07 |
Topics: generalized linear model and logistic model |
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第16週 |
6/11,6/14 |
Topics: smoothing techniques for curve fitting |
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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/ |
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