Empirical Process Theory and Applications

Spring semester 2021

General information

Lecturer Sara van de Geer
Assistant Corinne Emmenegger
Lectures Tuesday 08-10. The lectures take place on Zoom and the Zoom link can be found on Moodle.
Moodle >>
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


The following list contains further literature. The books can be downloaded from the ETH library; please see the provided link (you need to have a VPN connection running if you want to download them from home).

  • A. W. van der Vaart and J. A. Wellner. Weak convergence and empirical processes : with applications to statistics. Springer Series in Statistics. Springer, New York, 1996, [Online].
  • R. Vershynin. High-dimensional probability : an introduction with applications in data science. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2018, [Online].