Advanced Theory of Statistics
This course covers theoretical and applied fundamentals of statistical inference for beginning graduate students in statistics and probability. The main contents include statistical models, estimation, hypothesis testing, and asymptotic theory.
讲师
日期
2024年09月19日 至 12月31日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 15:20 - 16:55 | A14-202 | ZOOM A | 388 528 9728 | BIMSA |
修课要求
Calculus, Fundamentals of probability and statistics
课程大纲
Sampling Theory
Some special statistics
Distributions of special statistics
Point Estimation
Confidence Intervals for Means
Confidence Intervals for Differences of Means
Tests of Statistical Hypotheses
Additional Comments About Statistical Tests
Chi-Square Tests
Measures of Quality of Estimators
A Sufficient Statistic for a Parameter
Properties of a Sufficient Statistic
Completeness and Uniqueness
The Exponential Class of Distribution
Functions of a Parameter
The Case of Several Parameters
Minimal Sufficiency and Ancillary Statistics
Sufficiency, Completeness and Independence
Bayesian Estimation
Fisher Information and Rao-Cramér Inequality
Limiting Distributions of Maximum Likelihood
Certain Best Tests
Uniformly Most Powerful Tests
Likelihood Ratio Tests
The Distribution of Quadratic Forms
A Test of the Equality of Several Means (One-way ANOVA)
Noncentral chi-square and Noncentral
Analysis of Variance (ANOVA)
Some special statistics
Distributions of special statistics
Point Estimation
Confidence Intervals for Means
Confidence Intervals for Differences of Means
Tests of Statistical Hypotheses
Additional Comments About Statistical Tests
Chi-Square Tests
Measures of Quality of Estimators
A Sufficient Statistic for a Parameter
Properties of a Sufficient Statistic
Completeness and Uniqueness
The Exponential Class of Distribution
Functions of a Parameter
The Case of Several Parameters
Minimal Sufficiency and Ancillary Statistics
Sufficiency, Completeness and Independence
Bayesian Estimation
Fisher Information and Rao-Cramér Inequality
Limiting Distributions of Maximum Likelihood
Certain Best Tests
Uniformly Most Powerful Tests
Likelihood Ratio Tests
The Distribution of Quadratic Forms
A Test of the Equality of Several Means (One-way ANOVA)
Noncentral chi-square and Noncentral
Analysis of Variance (ANOVA)
参考资料
Introduction to Mathematical Statistics by Robert V. Hogg and Allen T. Craig
Statistical Inference by Casella and Berger
Mathematical Statistics by J. Shao
Statistical Inference by Casella and Berger
Mathematical Statistics by J. Shao
听众
Advanced Undergraduate
, Graduate
视频公开
不公开
笔记公开
不公开
语言
中文
, 英文
讲师介绍
赵鑫，现任北京雁栖湖应用数学研究院副研究员。研究兴趣主要集中于生物数学、计算生物学与人工智能的交叉领域。目前已在Springer Nature出版学术专著1部，并在相关领域权威国际期刊发表SCI论文十余篇。作为项目负责人，主持完成国家自然科学基金青年科学基金项目（已结题）以及清华大学清峰项目2项（已结题）。作为主要参与人，参与完成国家自然科学基金重大研究计划、重点项目、面上项目及北京市自然科学基金等多项科研课题。长期承担数学与统计学课程教学工作，主讲课程包括数学分析、高等代数、概率论、数理统计、多元统计分析等。现为北京市战略科学家核心团队成员。曾获清华大学优秀博士毕业生、清华大学优秀博士学位论文、国家奖学金及综合优秀一等奖学金、若琳奖等荣誉。