Maximal asymptotic power and efficiency of two-sample tests based on generalized U-Statistics

In this article a systematic study is given of the asymptotic behavior of two-sample tests based on U-Statistics with arbitrary antisymmetric kernels . Besides the investigation under the hypothesis and under fixed alternatives we determine the local power as a function of as well as its maximizing value _opt. Moreover formulas for the asymptotic relative efficiency ARE(₂,₁) of the ₂-test with respect to the ₁-test are derived. It turns out that _opt also yields the most efficient test in the sense that ARE(_opt,)1 for all (admissible) kernels .     

Möglichkeiten und Grenzen der mathematischen Schadenmodellierung

Mathematical claims modelling is a traditional art of actuarial practice. However, changing expectations concerning the complexity and efficiency of mathematical models have lead to numerous developments in the recent years, particularly in the area of multivariate models. This goes hand in hand with questions about what is ?possible“ and what is ?meaningful“. Due to sophisticated improvements of the classical models, the one-dimensional situation is well-tractable today whenever sufficient data material is available. A more difficult task is the modelling of situations where data are sparse or, alternatively, highly complex. Here sometimes theoretical arguments have to be used for justification, as in the area of large claims or extreme values. A more modern approach to multivariate situations is via copulas which allow for a separation of the problem of marginal distributions and the joint dependence structure. However, so far there is little experience with such tools in the insurance world, which makes further scientific research necessary.