STAT711 | Statistical Theory 1
Fall 2023
Time: Tu/F 11-12:30am at SCB4402
Instructor
-
Donlapark Ponnoprat
Office: STB304
Gradings
- Assignments 35%
- Scribe note 5%
- Midterm exam 30%
- Final exam 30%
References
- Statistical Inference by Roger L. Casella, George Berger. Duxbury Press.
- Theoretical Statistics - Topics for a Core Course by Robert W. Keener. Springer.
- Robert Nowak’s lecture notes on Statistical Signal Processing and Learning Theory Link.
Lecture Notes
| No. | Topic | Notes | Homework |
|---|---|---|---|
| 1 | Basic set theory and probability | ||
| 2 | Counting | ||
| 3 | Conditional probability | ||
| 4 | Independence and random variables | ||
| 5 | Multiple random variables | ||
| 6 | Variance and Standard Deviation | Homework 1 | |
| 7 | Probability distributions | ||
| 8 | Probability density functions | ||
| 9 | Examples of probability distributions | ||
| 10 | Poisson and Normal distributions | ||
| 11 | Cumulative distribution functions | ||
| 12 | Marginal and conditional distributions, Independence | Homework 2 | |
| 13 | Transformation of random variables | ||
| 14 | Moments and MGF | ||
| 15 | Random samples | Lecture 15 | |
| 16 | Sample mean and sample variance | Lecture 16 | |
| 17 | Sufficient statistics | Lecture 17 | |
| 18 | Minimal sufficient statistics | Lecture 18 | Homework 3 |
| 19 | Complete statistics, Basu's theorem | Lecture 19 | |
| 20 | Rao-Blackwell theorem, UMVU | Lecture 20 | |
| 21 | Maximum Likelihood estimators | Lecture 21 | |
| 22 | Cramér-Rao inequality | Lecture 22 | |
| 23 | Bayesian inference | Lecture 23 | Homework 4 |
| 24 | Minimax estimators | Lecture 24 | |
| 25 | Neyman-Pearson lemma | Lecture 25 | |
| 26 | Monotone likelihood ratio tests | Lecture 26 | |
| 27 | Likelihood ratio tests | Lecture 27 | |
| 28 | Confidence intervals | Lecture 28 | Homework 5 |