Plausible prior estimation

The problem of selecting a prior distribution when it comes to Bayes estimation often constitutes a choice between conjugate or noninformative priors, since in both cases the resulting posterior Bayes estimator (PBE) can be solved analytically and is therefore easy to calculate. Nevertheless, some of the implicit assumptions made by choosing a certain prior can be difficult to justify when a concrete sample of small size has been drawn. For example, when the underlying distribution is assumed to be normal, there is no reason to expect that the true but unknown location parameter is located outside the range of the sample. So why should a distribution with a non-compact domain be used as a prior for the mean? In addition, if there is some skewness in a sample of small size due to outliers when a symmetric distribution is assumed, this finding can be used to correct the PBE when determining the hyperparameters. Both ideas are applied to an empirical Bayes approach called plausible prior estimation (PPE) in the case of estimating the mean of a normal distribution with known variance in the presence of outliers. We propose an approach for choosing a prior and its respective hyperparameters, taking into account the above mentioned considerations. The resulting influence function as a frequentistic measure of robustness is simulated. To conclude, several simulation studies have been carried out to analyze the frequentistic performance of the PPE in comparison to frequentistic and Bayes estimators in certain outlier scenarios

New concepts of symmetry for copulas

This paper introduces two new concepts of symmetry for multivariate copulas with a focus on tails regions. Properties of the symmetry concepts are investigated for bivariate copulas and a connection to radial symmetry is established. Two nonparametric testing procedures for the new concepts are developed using a vector of locally most powerful rank test statistics, applied to a new generalization of the FGM copula which parameterizes every vertex of the unit cube. This vector quantities deviations from independence in each vertex and the tests for the new symmetry concepts are based on comparisons of these deviations. It is shown that one of the new tests can also be used to test for radial symmetry, which results in a similar power of detecting bivariate radial symmetry compared to recently published nonparametric tests. Further, an application to insurance data is provided. Finally, an improvement of the selection process in the context of vine copula fitting is proposed that is based on the elimination of copula families with unsuitable symmetry properties.Wednesday 10th May, 201

Aus der Zeit gefallene Geschichtsschreibung : der vierte Band von Stolleis' Geschichte des öffentlichen Rechts behandelt die Bundesrepublik und die DDR

Rezension zu: Michael Stolleis : Geschichte des öffentlichen Rechts in Deutschland. Vierter Band, Staats- und Verwaltungsrechtswissenschaft in West und Ost 1945 – 1990 München 2012, C. H. Beck, ISBN 978-3-406-63203-7, 720 Seiten, 68 Euro