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Zitierlink DOI
10.26092/elib/1415

Non-parametric Statistical Methods - Applications in MALDI Imaging and Finance

Veröffentlichungsdatum
2022-01-28
Autoren
von Schroeder, Jonathan  
Betreuer
Dickhaus, Thorsten  
Gutachter
Bodnar, Taras  
Zusammenfassung
This thesis contains applications of (non-)parametric statistical methods (and the development of such techniques) with a focus on applications to three distinct topics:

1) Computational statistics, specifically the (efficient and exact) calculation of the joint distribution of order statistics. Since ranks are fundamental to many statistical methods, these have many applications, some of which are detailed.
2) Mathematical finance, specifically results on "reverse stress testing" which, roughly speaking, has the goal of performing a data-driven selection of likely scenarios for which a given portfolio exceeds a specified loss. Two notable contributions are the development of non-parametric confidence regions in elliptical models and a characterisation of the subspace which, in skew-elliptical models, contains the sought scenario.
3) Mathematical statistics, specifically methods with applications to the statistical analysis of biomedical images. One focus is on statistical tests based on correlation coefficients when one of the random variables is a binary random variable. The derived results are utilised to elucidate some statistical properties of matrix-assisted laser desorption/ionization (MALDI) mass spectroscopy data.

In my work on all of these topics, my focus was on developing and applying statistical methods that are based only on the absolutely necessary assumptions. This is, of course, an aspirational goal. I am, however hopeful that I was able to make my own small contribution to the science of mathematical statistics.
Schlagwörter
non-parametric statistics

; 

mathematical finance

; 

computational statistics
Institution
Universität Bremen  
Fachbereich
Fachbereich 03: Mathematik/Informatik (FB 03)  
Dokumenttyp
Dissertation
Zweitveröffentlichung
Nein
Lizenz
https://creativecommons.org/licenses/by/4.0/
Sprache
Englisch
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Dissertation - Jonathan von Schroeder - Non-parametric Statistical Methods - Applications in MALDI Imaging and Finance.pdf

Size

1.79 MB

Format

Adobe PDF

Checksum

(MD5):1591158188cde109aa3f98d5696228a2

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