Theoretical Statistics III · Statistics
Empirical Process Theory: VC classes, Glivenko-Cantelli, Donsker, Chaining, etc.
Advanced topics in theoretical statistics especially relevant to high dimensional problems, including concentration inequalities and random matrix theory.
This course, Empirical Process Theory by Prof. Bodhisattva Sen, covers the fundamental theory of empirical processes. It covers basic concentration inequalities, notions to define size of function classes, Glivenko-Cantelli classes, Talagrand's concentration for the suprema of empirical processes, and finally touches on weak convergence and Donsker classes. Throughout the courses applications of this theory to statistical problems like M-estimators is impressed upon.
Empirical processes and some of its applications in high-dimensional statistics/non-parametric statistics
If you are interested in inference this class is a must.
After taking the course, I feel more comfortable when seeing some empirical process arguments in papers.
Low workload (although if you want to learn things well you have to pay more effort), high-quality lectures, very nice professor. Although we didn't dig into some topics very deeply, most of the important and useful stuff (like various maximal inequalities, VC theory, concentration inequalities and weak convergence) are touched. Very useful for my research (I'm doing statistical machine learning). 1 Columbia University: Arts & Sciences Fall 2021 Course: STATGR6203_001_2021_3-THEORETICALSTATISTICSIII : STATGR6203_001_2021_3 - THEORETICAL STATISTICS III Instructor: Bodhisattva Sen