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Mathematical and Nonparametric Statistics
(dt. Mathematische und nichtparametrische Statistik)

Level, degree of commitment Specialization module, depends on importing study program
Forms of teaching and learning,
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Business Mathematics.
Subject, Origin Mathematics, M.Sc. Business Mathematics, M.Sc. Business Mathematics
One semester,
Regularly alternating with other specialization modules
Person in charge of the module's outline Prof. Dr. Hajo Holzmann


  • Statistical models, moment estimators and maximum likelihood estimators, sufficiency of statistics, exponential families,
  • Fundamentals of decision theory, Unbiased estimation and the theorems of Rao - Blackwell and Lehman - Scheffe,
  • Minimax - and Bayes approach, Shrinkage estimation and oracle inequalities,
  • test theory, Neyman-Pearson lemma, UMP and UMPU tests
  • nonparametric density and regression estimation, asymptotic minimax optimality theory

Qualification Goals

The students

  • Know the basic concepts of mathematical and nonparametric statistics,
  • are familiar with some important statistical procedures and can apply them using the statistical software R,
  • have deepened mathematical working methods (developing mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills in exercises by practicing free speech in front of an audience and in discussion.


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, Statistics, Probability Theory.

Recommended Reading

  • Trabs, M., Jirak, M., Krenz, K., Reiß, M., "Statistik und maschinelles Lernen", Springer 2020
  • Shao, J., „Mathematical Statistics“, Springer 2003.
  • Tsybakov, A., "Introduction to Nonparametric Estimation", Springer, 2009

Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. 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

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.