This course is about the mathematics of high dimensional and infinite dimensional statistical models. The former are characterized by a number of parameters that may exceed the available sample size, and the latter are also known as "nonparametric" models. In both cases, we will emphasize results that are "nonasymptotic" in the sense that they are meaningful for fixed sample sizes, as opposed to limit theorems for the sample size growing to infinity.

Prerequisites: Standard undergraduate analysis and linear algebra. Basic notions of measure theoretic probability (including conditional expectation). Basic facts about Banach and Hilbert spaces. We will require no specific results from introductory mathematical statistics, but knowing what statistics is all about will help, of course.

(Please check for updates.)