Data sets from car insurance companies often have a high-dimensional complex dependency structure. The use of classical statistical methods such as generalized linear models or Tweedie?s compound Poisson model can yield problems in this case. Christmann (2004) proposed a general approach to...

The regression depth method (RDM) proposed by Rousseeuw and Hubert [RH99] plays an important role in the area of robust regression for a continuous response variable. Christmann and Rousseeuw [CR01] showed that RDM is also useful for the case of binary regression. Vapnik?s convex risk...

We investigate properties of kernel based regression (KBR) methods which are inspired by the convex risk minimization method of support vector machines. We first describe the relation between the used loss function of the KBR method and the tail of the response variable Y . We then establish a...

Many robust statistical procedures have two drawbacks. Firstly, they are computer-intensive such that they can hardly be used for massive data sets. Secondly, robust confidence intervals for the estimated parameters or robust predictions according to the fitted models are often unknown. Here, we...

The optimization of the hyper-parameters of a statistical procedure or machine learning task is a crucial step for obtaining a minimal error. Unfortunately, the optimization of hyper-parameters usually requires many runs of the procedure and hence is very costly. A more detailed knowledge of the...

Some methods from statistical machine learning and from robust statistics have two drawbacks. Firstly, they are computer-intensive such that they can hardly be used for massive data sets, say with millions of data points. Secondly, robust and non-parametric confidence intervals for the...

The goals of this paper are twofold: we describe common features in data sets from motor vehicle insurance companies and we investigate a general strategy which exploits the knowledge of such features. The results of the strategy are a basis to develop insurance tariffs. The strategy is applied...

The paper brings together methods from two disciplines: machine learning theory and robust statistics. Robustness properties of machine learning methods based on convex risk minimization are investigated for the problem of pattern recognition. Assumptions are given for the existence of the...

The behaviour of group sequential tests in the two-sample problem is investigated if one replaces the classical non-robust estimators in the t-test statistic by modern robust estimators of location and scale. Hampel's 3-part redescending M-estimator 25A used in the Princeton study and the robust...

The minimum number of misclassifications achievable with affine hyper_ planes on a given set of labeled points is a key quantity in both statistics and computational learning theory. However, determining this quantity exactly is essentially NP_hard_ cf_ Höfgen, Simon and van Horn (1995.) Hence,...