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Empirical processes
(dt. Empirische Prozesse)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Oral examination (individual examination) or written examination
Language,
Grading		 English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Business Mathematics.
Duration,
frequency		 One semester,
I.d.R. in jedem vierten Semester
Person in charge of the module's outline Prof. Dr. Hajo Holzmann

Contents

  • Empirical processes and partial sum processes.
  • Symmetrization and Vapnik-Chervonenki's theory.
  • Applications to empirical risk reduction
  • Glivenko-Cantelli theorems
  • Convergence of stochastic processes with bounded paths
  • The classical Donsk theorems
  • Maximal inequalities and chaining
  • The uniform central limit theorem
  • Applications in asymptotic statistics

Qualification Goals

Translation is missing, sorry. German original:

Die Studierenden

  • können die Theorie empirischer Prozesse und der Konvergenz stochastischer Prozesse grundlegend darstellen und anwenden,
  • beherrschen Anwendungen auf statistische Fragestellungen,
  • können grundlegende Konzepte und Fragestellungen eines aktuellen wissenschaftlichen Gebiets beschreiben und deren Relevanz für die wissenschaftliche Praxis erläutern,
  • können komplexere mathematische Arbeitsweisen (Entwickeln von mathematischer Intuition und deren formaler Begründung, Abstraktion, Beweisführung) anwenden,
  • sind in der Lage, fachliche Themen frei vor einem fachlichen Publikum vorzustellen und zu diskutieren.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Probability Theory.


Applicability

Module imported from M.Sc. Business Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics
  • LAaG Mathematics

When studying B.Sc. Business Mathematics, this module can be attended in the study area Free Compulsory Elective Modules.


Recommended Reading

  • Dümbgen, Lutz (2010). Empirische Prozesse. Skript Univ. Bern
  • Kosorok, Michael (2008). Introduction to Empirical Processes and Semiparametric Inference. Springer.
  • Pollard, David (1984). Convergence of Stochastic Processes. Available online.
  • Pollard, David (1990). Empirical Processes: Theory and Applications. Available online.
  • van der Vaart, Aad and Wellner, Jon (1996).
  • Weak Convergence and Empirical Processes - With Application to Statistics. Springer.



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2025/26. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23 (no corresponding element)
  • Winter 2023/24
  • Winter 2025/26

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.