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