Dimension reduction techniques for functional data analysis model and approximate smooth random functions by lower dimensional objects. In many applications the focus of interest lies not only in dimension reduction but also in the dynamic behaviour of the lower dimensional objects. The most...

Predicting default probabilities is important for firms and banks to operate successfully and to estimate their specific risks. There are many reasons to use nonlinear techniques for predicting bankruptcy from financial ratios. Here we propose the so called Support Vector Machine (SVM) to...

Graphical data representation is an important tool for model selection in bankruptcy analysis since the problem is highly non-linear and its numericalrepresentation is much less transparent. In classical rating models a convenientrepresentation of ratings in a closed form is possible reducing...

Recently, Frittelli and Scandolo ([9]) extend the notion of risk measures, originally introduced by Artzner, Delbaen, Eber and Heath ([1]), to the risk assessment of abstract financial positions, including pay offs spread over different dates, where liquid derivatives are admitted to serve as...

This paper may be understood as a continuation of Topsøe’s seminal paper ([16]) to characterize, within an abstract setting, compact subsets of finite inner regular measures w.r.t. the weak topology. The new aspect is that neither assumptions on compactness of the inner approximating lattices...

Let W denote a family of probability distributions with parameter space t, and WG be a subfamily of W depending on a mapping G : O -- t. Extremum estimations of the parameter vector v e O are considered. Some sufficient conditions are presented to ensure the uniqueness with probability one. As...

In semiparametric models it is a common approach to under-smooth the nonparametric functions inorder that estimators of the finite dimensional parameters can achieve root-n consistency. The requirementof under-smoothing may result as we show from inefficient estimation methods or technical...

Population forecasts are crucial for many social, political and economic decisions. Officialpopulation projections rely in general on deterministic models which use different scenariosfor future vital rates to indicate uncertainty. However, this technique shows substantialweak points such as...