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
ED  - AitSahlia, Farid
T1  - Allocating and forecasting changes in risk
JF  - Journal of risk
N2  - We consider time-dependent portfolios and discuss the allocation of changes in the risk of a portfolio to changes in the portfolio’s components. For this purpose we adopt established allocation principles. We also use our approach to obtain forecasts for changes in the risk of the portfolio’s components. To put the approach into practice we present an implementation based on the output of a simulation. Allocation is illustrated with an example portfolio in the context of Solvency II. The quality of the forecasts is investigated with an empirical study.
KW  - portfolio risk
KW  - allocation
KW  - forecast
KW  - covariance principle
KW  - conditional expectation principle
Y1  - 2023
U6  - http://dx.doi.org/10.21314/JOR.2022.048
SN  - 1755-2842
SN  - 1465-1211
VL  - 25
IS  - 3
SP  - 1
EP  - 24
PB  - Infopro Digital Risk
CY  - London
ER  - 
TY  - JOUR
A1  - Gaigall, Daniel
T1  - On the applicability of several tests to models with not identically distributed random effects
JF  - Statistics : A Journal of Theoretical and Applied Statistics
N2  - We consider Kolmogorov–Smirnov and Cramér–von-Mises type tests for testing central symmetry, exchangeability, and independence. In the standard case, the tests are intended for the application to independent and identically distributed data with unknown distribution. The tests are available for multivariate data and bootstrap procedures are suitable to obtain critical values. We discuss the applicability of the tests to random effects models, where the random effects are independent but not necessarily identically distributed and with possibly unknown distributions. Theoretical results show the adequacy of the tests in this situation. The quality of the tests in models with random effects is investigated by simulations. Empirical results obtained confirm the theoretical findings. A real data example illustrates the application.
KW  - central symmetry test
KW  - exchangeability test
KW  - independence test
KW  - random effects
KW  - not identically distributed
Y1  - 2023
SN  - 0323-3944
U6  - http://dx.doi.org/10.1080/02331888.2023.2193748
SN  - 1029-4910
VL  - 57
PB  - Taylor & Francis
CY  - London
ER  - 
TY  - THES
A1  - Gaigall, Daniel
T1  - On selected problems in multivariate analysis
N2  - Selected problems in the field of multivariate statistical analysis are treated. Thereby, one focus is on the paired sample case. Among other things, statistical testing problems of marginal homogeneity are under consideration. In detail, properties of Hotelling‘s T² test in a special parametric situation are obtained. Moreover, the nonparametric problem of marginal homogeneity is discussed on the basis of possibly incomplete data. In the bivariate data case, properties of the Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic on the basis of partly not identically distributed data are investigated. Similar testing problems are treated within the scope of the application of a result for the empirical process of the concomitants for partly categorial data. Furthermore, testing changes in the modeled solvency capital requirement of an insurance company by means of a paired sample from an internal risk model is discussed. Beyond the paired sample case, a new asymptotic relative efficiency concept based on the expected volumes of multidimensional confidence regions is introduced. Besides, a new approach for the treatment of the multi-sample goodness-of-fit problem is presented. Finally, a consistent test for the treatment of the goodness-of-fit problem is developed for the background of huge or infinite dimensional data.
KW  - Paired sample
KW  - Marginal homogeneity
KW  - Incomplete data
KW  - Asymptotic relative efficiency
KW  - Volumes of confidence regions
Y1  - 2023
U6  - http://dx.doi.org/10.15488/14304
N1  - Gottfried Wilhelm Leibniz Universität Hannover
ER  -