STAT711 | Statistical Theory 1

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	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