Publications and Preprints
Some notes on extremal discriminant analysis
Manjunath B.G., Melanie Frick and Rolf-Dieter Reiss
Classical discriminant analysis focusses 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 article 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.
Our 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.
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