STAT711 | Statistical Theory 1
Fall 2020
Time: Tu/F 11-12:30am in Microsoft Teams
Instructor
-
Donlapark Ponnoprat
Office: STB304 -
Manachai Rodchuen
E-mail:manachai.r--at--cmu.ac.th
Office: STB112
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
Lecture | Topic | Notes | Homework |
---|---|---|---|
1 | Basic set theory and probability | Lecture 1 | |
2 | Counting | Lecture 2 | |
3 | Conditional probability | Lecture 3 | |
4 | Independence and random variables | Lecture 4 | |
5 | Multiple random variables | Lecture 5 | |
6 | Variance and Standard Deviation | Lecture 6 | Homework 1 |
7 | Probability distributions | Lecture 7 | |
8 | Probability density functions | Lecture 8 | |
9 | Examples of probability distributions | Lecture 9 | |
10 | Poisson and Normal distributions | Lecture 10 | |
11 | Cumulative distribution functions | Lecture 11 | |
12 | Marginal and conditional distributions, Independence | Lecture 12 | Homework 2 |
13 | Transformation of random variables | Lecture 13 | |
14 | Moments and MGF | Lecture 14 | |
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 |