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

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 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: Written or oral examination (individual 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,
irregular
Person in charge of the module's outline Prof. Dr. Hajo Holzmann

Contents

  • 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

Translation is missing, sorry. German original:

Die Studierenden

  • können die Grundbegriffe der mathematischen und nichtparametrischen Statistik schildern,
  • können einige wichtigen Verfahren der Statistik erklären und sie mit der Statistik-Software R anwenden,
  • haben mathematische Arbeitsweisen (Entwickeln von mathematischer Intuition und deren formaler Begründung, Abstraktion, Beweisführung) vertieft,
  • haben in den Übungen ihre mündliche Kommunikationsfähigkeit durch Einüben der freien Rede vor einem Publikum und bei der Diskussion verbessert.

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, Elementary Probability and Statistics, Internship Stochastics, Statistics and Statistical Learning.


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. Data Science
  • M.Sc. Computer Science
  • 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

  • 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 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.