Extremal discriminant analysis

The main goal of this dissertation is to introduce an extreme value model to discriminant analysis. A classical discriminant analysis focuses on Gaussian and nonparametric models where in the second case, the unknown densities are replaced by kernel densities based on the training sample. In the present text we assume that it suffices to base the classification on exceedances above higher thresholds, which can be interpreted as observations in a conditional framework. Therefore, the statistical modeling of truncated distributions is merely required. In this context, a nonparametric modeling is not adequate because the kernel method is inaccurate in the upper tail region. Yet one may deal with truncated parametric distributions like the Gaussian ones. The primary aim is to replace truncated Gaussian distributions by appropriate generalized Pareto distributions and to explore properties and the relationship of discriminant functions in both models. Different to the classical work on discriminant analysis, we are also interested in the convergence of the classical discriminant function.