Mathematical Statistics I
This course offers a systematic introduction to the theory of mathematical statistics, based on the first three chapters of Shao's Mathematical Statistics. It begins with the essential probabilistic foundations and then develops the core principles of statistical inference, including sufficiency and completeness, loss and risk, and the main approaches to point estimation, hypothesis testing, and confidence sets. Topics in unbiased estimation are also covered, with attention given to both finite-sample and asymptotic properties of estimators and tests.
Lecturer
Date
2nd September ~ 25th November, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 16:55 | A3-3-201 | ZOOM 14 | 712 322 9571 | BIMSA |
Prerequisite
Fundamentals of Probability Theory
Syllabus
1. Preliminaries
2. Foundations of Probability
3. Asymptotic Theory and Conditioning
4. Statistical Models and Data Reduction
5. Principles of Statistical Inference
6. Theory of Unbiased Estimation
7. Estimation in Linear and Nonparametric Models
2. Foundations of Probability
3. Asymptotic Theory and Conditioning
4. Statistical Models and Data Reduction
5. Principles of Statistical Inference
6. Theory of Unbiased Estimation
7. Estimation in Linear and Nonparametric Models
Reference
[1] Shao, J., Mathematical Statistics, 2nd ed., New York: Springer, 2003.
[2] 茆诗松, 王静龙, 濮晓龙, 高等数理统计, 第3版, 北京: 高等教育出版社, 2022.
[2] 茆诗松, 王静龙, 濮晓龙, 高等数理统计, 第3版, 北京: 高等教育出版社, 2022.
Audience
Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
No
Language
Chinese
Lecturer Intro
Sixu Liu received her Ph.D. degree from Peking University in 2019. She then worked as a postdoc at Tsinghua University before joining BIMSA as an assistant professor in 2022. Her main research interests include dynamical systems and ergodic theory, as well as statistical experimental design.