Advanced Topics in Statistics (461-0-20)

Topic

Advanced Statistical Theory 2

Instructors

Matey Neykov

Meeting Info

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

Overview of class

Topic: Advanced Statistical Theory 2

This class is a continuation of STAT 461-0 Advanced Topics in Statistics: Advanced Statistical Theory 1. The first half of the class will be devoted to minimax lower bounds for estimation and testing. These bounds include strategies based on Le Cam's approach, Fano's inequality, Yang and Barron's construction and Assouad's inequality. Additional topics covered by the course include: Uniform Law of Large Numbers, VC theory, matrix concentration inequalities. We will further read and present the results of some selected papers in high-dimensional statistics.

Registration Requirements

The prerequisites include linear algebra, real analysis, a statistics theory class (e.g. Casella and Berger level) and Advanced Statistical Theory 1

Learning Objectives

The student will be able to read and understand modern papers in high-dimensional statistics; The student will also be equipped with tools to do their own research in the area.

Teaching Method

lectures

Evaluation Method

There will be 1-2 homework assignments + project (which will be writing a report on a selected by the student paper in high-dimensional/nonparametric statistics) and a class presentation

Class Materials (Required)

Main refernece: High-dimensional Statistics: A non-asymptotic viewpoint by Martin Wainwright
Other references: John Ducci's lecture notes (https://web.stanford.edu/class/stats311/lecture-notes.pdf)
High-dimensional probability by Roman Vershynin
Introduction to nonparametirc estimation by Alexandre Tsybakov

Class Notes

This is a must take for anyone who wants to do research in the area of high-dimensional statistics.