Cramér-von-Mises tests for the distribution of the excess over a confidence level

  • The Cramér-von-Mises distance is applied to the distribution of the excess over a confidence level. Asymptotics of related statistics are investigated, and it is seen that the obtained limit distributions differ from the classical ones. For that reason, quantiles of the new limit distributions are given and new bootstrap techniques for approximation purposes are introduced and justified. The results motivate new one-sample goodness-of-fit tests for the distribution of the excess over a confidence level and a new confidence interval for the related fitting error. Simulation studies investigate size and power of the tests as well as coverage probabilities of the confidence interval in the finite sample case. A practice-oriented application of the Cramér-von-Mises tests is the determination of an appropriate confidence level for the fitting approach. The adoption of the idea to the well-known problem of threshold detection in the context of peaks over threshold modelling is sketched and illustrated by data examples.

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Author:Daniel Gaigall, Julian Gerstenberg
ISSN:1048-5252 (Print)
ISSN:1029-0311 (Online)
Parent Title (English):Journal of Nonparametric Statistics
Publisher:Taylor & Francis
Document Type:Article
Year of Completion:2023
Date of the Publication (Server):2023/03/07
Tag:Cramér-von-Mises test; conditional excess distribution; confidence interval; goodness-of-fit test
Institutes:FH Aachen / Fachbereich Medizintechnik und Technomathematik
collections:Verlag / Taylor & Francis