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  - 
TY  - JOUR
A1  - Gaigall, Daniel
A1  - Gerstenberg, Julian
A1  - Trinh, Thi Thu Ha
T1  - Empirical process of concomitants for partly categorial data and applications in statistics
JF  - Bernoulli
N2  - On the basis of independent and identically distributed bivariate random vectors, where the components are categorial and continuous variables, respectively, the related concomitants, also called induced order statistic, are considered. The main theoretical result is a functional central limit theorem for the empirical process of the concomitants in a triangular array setting. A natural application is hypothesis testing. An independence test and a two-sample test are investigated in detail. The fairly general setting enables limit results under local alternatives and bootstrap samples. For the comparison with existing tests from the literature simulation studies are conducted. The empirical results obtained confirm the theoretical findings.
KW  - bootstrap
KW  - Categorial variable
KW  - Concomitant
KW  - Empirical process
KW  - Independence test
Y1  - 2022
U6  - http://dx.doi.org/10.3150/21-BEJ1367
SN  - 1573-9759
VL  - 28
IS  - 2
SP  - 803
EP  - 829
PB  - International Statistical Institute
CY  - Den Haag, NL
ER  -