Robust regression credibility: The influence function approach

In classical credibility theory we assume that the vector of claims conditionally on has independent components with identical means. However, this assumption is sometimes unrealistic. To relax this condition Hachemeister (Hachemeister, C.A., 1975. Credibility for regression models with application to trend. In: Kahn, P. (Ed.), Credibility, Theory and Applications. Academic Press, New York) introduced regressors. The presence of large claims can perturb the credibility premium estimation. The lack of robustness of regression credibility estimators, as well as the fairness of tariff evaluation, led to the development of this paper. Our proposal is to apply robust statistics to the regression credibility estimation by using the robust influence function approach of M-estimators.     

Operational risk: Emerging markets,sectors and measurement

The role of decision support systems in mitigating operational risks in firms is well established. However, there is a lack of investment in decision support systems in emerging markets, even though inadequate operational risk management is a key cause of discouraging external investment. This has also been exacerbated by insufficient understanding of operational risk in emerging markets, which can be attributed to past operational risk measurement techniques, limited studies on emerging markets and inadequate data.     

Topological mixing in -spaces

If is a proper -space and a non-elementary discrete group of isometries acting properly discontinuously on it is shown that the geodesic flow on the quotient space is topologically mixing, provided that the generalized Busemann function has zeros on the boundary and the non-wandering set of the flow equals the whole quotient space of geodesics (the latter being redundant when is compact). Applications include the proof of topological mixing for (A) compact negatively curved polyhedra, (B) compact quotients of proper geodesically complete -spaces by a one-ended group of isometries and (C) finite -dimensional ideal polyhedra.

     

A Lie symmetry analysis and explicit solutions of the two‐dimensional ∞‐Polylaplacian

In this work, we consider the Lie point symmetry analysis of a strongly nonlinear partial differential equation of third order, the ∞‐Polylaplacian, in two spatial dimensions. This equation is a higher order generalization of the ∞‐Laplacian, also known as Aronsson's equation, and arises as the analog of the Euler–Lagrange equations of a second‐order variational principle in L^∞. We obtain its full symmetry group, one‐dimensional Lie subalgebras and the corresponding symmetry reductions to ordinary differential equations. Finally, we use the Lie symmetries to construct new invariant ∞‐Polyharmonic functions.     

Multivariate Limited Translation Hierarchical Bayes Estimators

Based on the notion of predictive influence functions, the paper develops multivariate limited translation hierarchical Bayes estimators of the normal mean vector which serve as a compromise between the hierarchical Bayes and maximum likelihood estimators. The paper demonstrates the superiority of the limited translation estimators over the usual hierarchical Bayes estimators in terms of the frequentist risks when the true parameter to be estimated departs widely from the grand average of all the parameters.     

An optimal Hardy–Morrey inequality

In this work we improve the sharp Hardy inequality in the case p?>?n by adding an optimal weighted H?lder seminorm. To achieve this we first obtain a local improvement. We also obtain a refinement of both the Sobolev inequality for p?>?n and the Hardy inequality, the latter having the best constant.     

On the limiting distribution of sample central moments

We investigate the limiting behavior of sample central moments, examining the special cases where the limiting (as the sample size tends to infinity) distribution is degenerate. Parent (non-degenerate) distributions with this property are called singular, and we show in this article that the singular distributions contain at most three supporting points. Moreover, using the delta-method, we show that the (second-order) limiting distribution of sample central moments from a singular distribution is either a multiple, or a difference of two multiples of independent Chi-square random variables with one degree of freedom. Finally, we present a new characterization of normality through the asymptotic independence of the sample mean and all sample central moments.