Empirical Process Theory and Applications

Spring semester 2020

General information

Lecturer Sara van de Geer
Assistant Jeffrey Näf
Lectures Thursday 08-10 HG D 1.2 >>
Course catalogue data >>

Course content

In this series of lectures, we will start with considering exponential inequalities, including concentration inequalities, for the deviation of averages from their mean. We furthermore present some notions from approximation theory, because this enables us to assess the modulus of continuity of empirical processes. We introduce e.g., Vapnik Chervonenkis dimension: a combinatorial concept (from learning theory) of the "size" of a collection of sets or functions. As statistical applications, we study consistency and exponential inequalities for empirical risk minimizers, and asymptotic normality in semi-parametric models. We moreover examine regularization and model selection.

Course materials

Chapter 6 Lecture
Chapter 7 Lecture
Chapter 8 Lecture
Chapter 9 Lecture
Chapter 10-1 Lecture
Chapter 10-2 Lecture
Chapter 11 Lecture
Chapter 12 Lecture
Overview Lecture

Course materials

Week Topic
Week 1 Script
Week 6 Slides 6
Week 7 Slides 7
Week 8 Slides 8
Week 9 Slides 9
Week 10 Slides 10.1
Week 11 Slides 10.2
Week 12 Slides 11
Week 13 Slides 12

In-class exercises

A few times during the course, there will be in-class exercise sessions instead of a normal lecture. During those sessions, we will work with jupyter notebooks and R. These are provided in this Github repository.

Take-home exercises

If you are a PhD student who needs ETH credit points, the submission of the solutions is mandatory. If this applies to you, please email your solutions to Loris Michel or place them in the corresponding tray in HG J 68. Students who need ECTS credit points have to take the exam.

Exercises Solutions Due date
Series 1 Solutions 1 TBA