Advanced Topics in Statistics (461-0-20)

Topic

Advanced Statistical Theory 1

Instructors

Matey Neykov

Meeting Info

Parkes Hall 214: Mon, Wed 12:30PM - 1:50PM

Overview of class

This is the first part of a Ph.D. course in theoretical statistics. We will cover a selection of modern topics in mathematical statistics, with a focus on high-dimensional statistical models and nonparametric statistical models. One of the main goals of this course is to provide you with some theoretical background and mathematical tools to read and understand the current statistical literature on high-dimensional models.

Registration Requirements

calculus, intermediate statistics class (e.g. Casella and Berger level), linear algebra

Learning Objectives

the students will learn concentration inequalities, covering and packing numbers, Dudley integral, comparison inequalities, sparse PCA and LASSO bounds

Teaching Method

Lectures

Evaluation Method

homework assignments, take home exam, scribe duties

Class Materials (Required)

Main Reference:
"High-dimensional statistics: A non-asymptotic viewpoint" by M. Wainwright

Class Materials (Suggested)

"High Dimensional Statistics" lecture notes by P. Rigollet and J-C Hu ̈tter
"An introduction to nonparametric estimation" by A. Tskybakov
"High-Dimensional Probability" by R. Vershynin
"Probability in High Dimension" lecture notes by R. van Handel
"Information-theoretic methods for high-dimensional statistics" by Y. Wu

Class Notes

This is an advanced statistical theory class. It aims to acquaint the student with theoretical tools which are often used in high-dimensional and nonparametric statistics. It's a must take for anyone who wants to do modern mathematical statistics research.