Fixed values versus empirical quantiles as thresholds in excess distribution modelling

verfasst von: Daniel Gaigall, Julian Gerstenberg
Abstract: Conditional excess distribution modelling is a widely used technique, in financial and insurance mathematics or survival analysis, for instance. Classical theory considers the thresholds as fixed values. In contrast, the use of empirical quantiles as thresholds offers advantages with respect to the design of the statistical experiment. Either way, the modeller is in a non-standard situation and runs in the risk of improper usage of statistical procedures. From both points of view, statistical planning and inference, a detailed discussion is requested. For this purpose, we treat both methods and demonstrate the necessity taking into account the characteristics of the approaches in practice. In detail, we derive general statements for empirical processes related to the conditional excess distribution in both situations. As examples, estimating the mean excess and the conditional Value-at-Risk are given. We apply our findings for the testing problems of goodness-of-fit and homogeneity for the conditional excess distribution and obtain new results of outstanding interest.
Organisationseinheit(en): House of Insurance
Externe Organisation(en): Fachhochschule Aachen
Goethe-Universität Frankfurt am Main
Typ: Artikel
Journal: Journal of Statistical Planning and Inference
Band: 238
Anzahl der Seiten: 21
ISSN: 0378-3758
Publikationsdatum: 08.02.2025
Publikationsstatus: Elektronisch veröffentlicht (E-Pub)
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Statistik und Wahrscheinlichkeit, Statistik, Wahrscheinlichkeit und Ungewissheit, Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.1016/j.jspi.2025.106276 (Zugang: Offen)

BibTeX

@article{693c78e94f1e47d6948459cb6f014937,
title = "Fixed values versus empirical quantiles as thresholds in excess distribution modelling",
abstract = "Conditional excess distribution modelling is a widely used technique, in financial and insurance mathematics or survival analysis, for instance. Classical theory considers the thresholds as fixed values. In contrast, the use of empirical quantiles as thresholds offers advantages with respect to the design of the statistical experiment. Either way, the modeller is in a non-standard situation and runs in the risk of improper usage of statistical procedures. From both points of view, statistical planning and inference, a detailed discussion is requested. For this purpose, we treat both methods and demonstrate the necessity taking into account the characteristics of the approaches in practice. In detail, we derive general statements for empirical processes related to the conditional excess distribution in both situations. As examples, estimating the mean excess and the conditional Value-at-Risk are given. We apply our findings for the testing problems of goodness-of-fit and homogeneity for the conditional excess distribution and obtain new results of outstanding interest.",
keywords = "Conditional excess distribution, Empirical quantile, Goodness-of-fit test, Homogeneity test",
author = "Daniel Gaigall and Julian Gerstenberg",
note = "Publisher Copyright: {\textcopyright} 2025 The Authors",
year = "2025",
month = feb,
day = "8",
doi = "10.1016/j.jspi.2025.106276",
language = "English",
volume = "238",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",
}