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This entry is from Summer semester 2021 and might be obsolete. No current equivalent could be found.
Nonparametric Statistics
(dt. Nichtparametrische Statistik)
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: Written or oral examination |
Language, Grading |
German or 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. Markus Bibinger, Prof. Dr. Hajo Holzmann |
Contents
- Non-parametric density estimation, core estimator, projection estimator, upper barriers for point by point, uniform and integrated risk
- Lower bounds and optimal rates
- Lepski's scheme and adaptivity
- Nonparametric regression, local polynomial estimators
- Model in white noise, Pinsker estimation and Pinsker constant
- Wavelet estimation
Qualification Goals
The students shall
- get an insight into a current research area of nonparametric statistics,
- acquire the basic techniques within the field of nonparametric statistics,
- practice mathematical methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof methods),
- improve their oral communication skills in the recitation classes by practicing free speech in front of an audience and during 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, Mathematical Statistics.
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
When studying B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.
The module is assigned to Applied Mathematics. Further information on eligibility can be found in the description of the study area.
Recommended Reading
- Tsybakov, A. (2009) Introduction to nonparametric estimation. Springer
- Johnstone, I. (2013) Gaussian estimation: Sequence and wavelet models.
Please note:
This page describes a module according to the latest valid module guide in Summer semester 2021. 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
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021
- Winter 2021/22
- Winter 2022/23
- Winter 2023/24 (no corresponding element)
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.