Dokument: Estimation, Testing and Pooling in Block Maxima Models for Climate Extremes
| Titel: | Estimation, Testing and Pooling in Block Maxima Models for Climate Extremes | |||||||
| URL für Lesezeichen: | https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=63018 | |||||||
| URN (NBN): | urn:nbn:de:hbz:061-20230717-112740-7 | |||||||
| Kollektion: | Dissertationen | |||||||
| Sprache: | Englisch | |||||||
| Dokumententyp: | Wissenschaftliche Abschlussarbeiten » Dissertation | |||||||
| Medientyp: | Text | |||||||
| Autor: | Zanger, Leandra [Autor] | |||||||
| Dateien: |
| |||||||
| Beitragende: | Prof. Dr. Bücher, Axel [Gutachter] Jun.-Prof. Dr. Oesting, Marco [Gutachter] | |||||||
| Stichwörter: | Extreme Value Statistics, Block Maxima, GEV Distribution | |||||||
| Dewey Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik » 510 Mathematik | |||||||
| Beschreibung: | Modelling climate extremes can be challenging due to short observation periods,which leads to unfavourably large estimation uncertainties.
In the widely used block maxima method, it has been found in several scenarios that estimation variance may be reduced if sliding blocks are used instead of disjoint blocks. This line of research is extended by examining the probability-weighted moment estimator for the parameter vector of the generalised extreme value distribution, based on both disjoint and sliding block maxima of univariate observations. In contrast to other results on the probability-weighted moment estimator from the literature, which usually consider independent and identically distributed observations, the assumptions on the underlying random variables are adapted to the setting of environmental applications, by assuming either stationarity or some kind of piecewise stationarity. For the latter setting, a proof of concept is provided that encourages the use of sliding block maxima despite their non-stationarity. The estimators are analysed both theoretically in an asymptotic framework and sub-asymptotically in a simulation study, showing increased efficiency of the sliding version in both analyses. For spatial data, the pooling approach is common for reducing estimation variance. It consists of combining spatial observations that are assumed to have some sort of homogeneous probabilistic behaviour. To avoid biased estimators, it is important to validate this homogeneity assumption in advance. New statistical significance tests for testing corresponding hypotheses are provided, which are based on multivariate generalised extreme value models. The underlying random variables are assumed to be serially, but not necessarily spatially, independent. Unlike many competing tests in the literature, the proposed tests take into account possible cross-correlations of the data. Tests are provided for the case of stationary models as well as models that exhibit a certain type of trend in their extremes. They are based on limiting distributions that are derived for estimators of the parameter vectors, and reliable p-values are obtained by means of parametric bootstrap procedures. Finite-sample properties are investigated in a simulation study. Further, a method for selecting a region that can be assumed homogeneous is provided, which is based on multiple testing. | |||||||
| Lizenz: |  Dieses Werk ist lizenziert unter einer Creative Commons Namensnennung 4.0 International Lizenz | |||||||
| Fachbereich / Einrichtung: | Mathematisch- Naturwissenschaftliche Fakultät » WE Mathematik » Mathematische Statistik und Wahrscheinlichkeitstheorie | |||||||
| Dokument erstellt am: | 17.07.2023 | |||||||
| Dateien geändert am: | 17.07.2023 | |||||||
| Promotionsantrag am: | 01.03.2023 | |||||||
| Datum der Promotion: | 22.06.2023 |
