Empirische Prozesse

Dozent und Übungsleiter: Michael Vogt

General Information


Lectures 2 h
Excercises 2 h

Lectures s. Moodle

Excercises s. Moodle  
Exam s. Moodle  

General Information:

Target Audience: 

  • Master Mathematische Biometrie
  • Master Wirtschaftsmathematik
  • Master Finance
  • Master Mathematik

Course Prerequisites: 

Elementary Probability Calculus and Statistics


The lecture deals with modern empirical process theory. Empirical process theory started in the 1930s and 1940s with the analysis of the empirical distribution function. Back then, the main interest focused on deriving uniform convergence statements for the empirical distribution function. Modern empirical process theory deals with general uniform convergence statements, in particular, with uniform laws of large numbers (Glivenko-Cantelli theorems) and uniform central limit theorems (Donsker theorems). It is an indispensable theoretical tool for many modern fields of statistics including non- and semiparametrics, high-dimensional statistics, machine learning and biostatistics.



  • A. Van der Vaart & J. Wellner (1996). Weak Convergence and Empirical Processes. Springer.
  • D. Pollard (1990). Empirical Processes: Theory and Applications. NSF-CBMS Regional Conference Series in Probability and Statistics: Volume 2.
  • G. Shorack & J. Wellner (1986). Empirical Processes with Applications to Statistics. Wiley.

Link zum Semesterapparat



This course will be held completely online (except for exams). Information and material will be provided on Moodle.


Prof. Dr. Michael Vogt

Institut of Statistics
Helmholtzstraße 20
89081 Ulm
Raum: HeHo 20 E.43