Empirische Prozesse

Lecturer: Michael Vogt

Exercises: Manuel Rosenbaum

General Information


Lectures 2 SWS
Excercises 1 SWS

Lectures: Wednesday 10:00 - 12:00, N24 Room 226

Excercises: Wednesday 14:00 - 16:00, Helmholtzstraße 18, Room 120  
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.