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.
Lecturer
Date
19th September ~ 31st December, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 15:20 - 16:55 | A14-202 | ZOOM A | 388 528 9728 | BIMSA |
Prerequisite
Calculus, Fundamentals of probability and statistics
Syllabus
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)
Reference
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
Audience
Advanced Undergraduate
, Graduate
Video Public
No
Notes Public
No
Language
Chinese
, English