STAT711  Statistical Theory 1
Fall 2020
Time: Tu/F 1112:30am in Microsoft Teams
Instructor

Donlapark Ponnoprat
Office: STB304 
Manachai Rodchuen
Email:manachai.ratcmu.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  RaoBlackwell theorem, UMVU  Lecture 20  
21  Maximum Likelihood estimators  Lecture 21  
22  CramérRao inequality  Lecture 22  
23  Bayesian inference  Lecture 23  Homework 4 
24  Minimax estimators  Lecture 24  
25  NeymanPearson lemma  Lecture 25  
26  Monotone likelihood ratio tests  Lecture 26  
27  Likelihood ratio tests  Lecture 27  
28  Confidence intervals  Lecture 28  Homework 5 