Statistics · Columbia University
- I had a good knowledge of probability from my undergrad degree, so the course was more of a refresher than anything
math statistic, more related the fundamental of statistic theorem
Empirical Process Theory: VC classes, Glivenko-Cantelli, Donsker, Chaining, etc.
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.
The concepts are vivid and engaging. In-depth inferential concepts have been addressed and the flow of the course is commendable. However, the half-semester element does hinder a complete understanding under the time constraint.
Recommended if you are new to probability.
We went over what a statistic is, how to estimate the mean/variance of different distributions and what the "best" estimator is, and then statistical inferences, hypothesis testing, confidence intervals, and ended with an overview of linear regression.
Empirical processes and some of its applications in high-dimensional statistics/non-parametric statistics
Methods of estimation (i.e., MLE, MOM, Bayesian method), Hypothesis testing, N.P. Lemma. etc...
If you are interested in inference this class is a must.