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401-4627-00L 4 Credits BSC , MSC D-MATH
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Empirical Process Theory and Applications

Lecturers & Examiners: Prof. Dr. Yuansi Chen
VVZ CR n/a

Last Updated: 2026-06-01 11:31:23

Abstract

Empirical process theory provides a rich toolbox for studying the properties of empirical risk minimizers, such as least squares and maximum likelihood estimators, support vector machines, etc.

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.

Resources

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 120 minutes
Aids
None
The written exam is offered only in the two sessions immediately following the course: Winter 2026 and Summer 2026.

Course Components

Type Title Time & Place Hours
lecture Empirical Process Theory and Applications
  • Mon 14:15-16:00 (HG D 5.2)
2 h weekly

Offered In