STAT583: Advanced Theory of Statistical Inference (2018)

This is a 10-week course focused on introducing advanced mathematical tools for statisticians, and more generally, researchers who work on stochastic models and are interested in understanding the driving forces beneath them.

Check the Syllabus for detailed course plan.


Instructor: Fang Han (

Grader: Yandi Shen ( and Hongjian Shi (

Lectures: 10:30AM-11:20AM (M&W&F, MGH-271)

Office hour: 11:30AM-12:30PM (M, PDL B-308)

Lecture notes:

Lecture note 1

Lecture note 1 (addendum)

Proof of ASN of sample quantiles

Galen's one-page proof of Kiefer's "mysterious" theorem

Massart's DKW Inequality of tight constant

Lecture note 2

Lecture note 3

Homework assigments:

Homework 1

Homework 2

Homework 3

Final project:

Please pick one of the following papers, rephrase and write down the proof of the pointed main theorem(s) in it. The project will be evaluated by your written report. (If you wish to pick a paper outside of the given pool, please consult the instructor.) The project is due on 11:59PM on 06/07/2018. No free day is allowed.

1. Massart's DKW Inequality of tight constant;

2. Royen's proof of Gaussian correlation inequality;

3. Theorem 7 in Nolan and Pollard's U-processes theory;

4. Theorems 3.1 and 3.2 in Guntuboyina and Sen's construction proof of convex function's covering number;

5. Theorem 5.1 in Duembgen's analysis of Tyler's M-estimator;

6. Results in Section 2.1 in Chen and Wellner's analysis of convex least squares.

Suggested reading:

1. Some useful inequalities (last update: 1PM, 03/27)

2. Appendix A (Inequalities and Miscellaneous) in "Empirical Processes with Applications to Statistics", by Galen Shorack and Jon Wellner

3. Appendix A in "Weak Convergence and Empirical Processes", by Aad van der Vaart and Jon Wellner

4. Minimax theory (last update: 1PM, 05/26)

5. Kosorok's Bios 791 lecture notes (last update: 1PM, 05/26)