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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		 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)
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,
Regularly alternating with other specialization modules
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

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.

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, Statistics, Probability Theory.


Applicability

The module 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 M.Sc. Business Mathematics, this module can be attended in the study area Free Compulsory Elective Modules.

The module can also be used in other study programs (export module).


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.