TY  - JOUR
A1  - Gaigall, Daniel
A1  - Gerstenberg, Julian
T1  - Cramér-von-Mises tests for the distribution of the excess over a confidence level
JF  - Journal of Nonparametric Statistics
N2  - 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.
KW  - Cramér-von-Mises test
KW  - conditional excess distribution
KW  - confidence interval
KW  - goodness-of-fit test
Y1  - 2023
U6  - http://dx.doi.org/10.1080/10485252.2023.2173958
SN  - 1048-5252 (Print)
SN  - 1029-0311 (Online)
PB  - Taylor & Francis
ER  -