@article{GaigallGerstenbergTrinh2022,
  author    = {Gaigall, Daniel and Gerstenberg, Julian and Trinh, Thi Thu Ha},
  title     = {Empirical process of concomitants for partly categorial data and applications in statistics},
  series = {Bernoulli},
  volume    = {28},
  journal   = {Bernoulli},
  number    = {2},
  publisher = {International Statistical Institute},
  address   = {Den Haag, NL},
  issn      = {1573-9759},
  doi       = {10.3150/21-BEJ1367},
  pages     = {803 -- 829},
  year      = {2022},
  abstract  = {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.},
  language  = {en}
}
@article{Gaigall2021,
  author    = {Gaigall, Daniel},
  title     = {Test for Changes in the Modeled Solvency Capital Requirement of an Internal Risk Model},
  series = {ASTIN Bulletin},
  volume    = {51},
  journal   = {ASTIN Bulletin},
  number    = {3},
  publisher = {Cambridge Univ. Press},
  address   = {Cambridge},
  issn      = {1783-1350},
  doi       = {10.1017/asb.2021.20},
  pages     = {813 -- 837},
  year      = {2021},
  abstract  = {In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.},
  language  = {en}
}