Some notes on extremal discriminant analysis

• Published in: Journal of multivariate analysis Vol. 103; no. 1; pp. 107 - 115
• Main Authors: Manjunath, B.G., Frick, Melanie, Reiss, Rolf-Dieter
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 2012; Elsevier; Taylor & Francis LLC
• Series: Journal of Multivariate Analysis
• Subjects: Discriminant analysis; Discriminant analysis Gaussian model Truncation Generalized Pareto distributions Linear discriminant functions Husler-Reiss triangular arrays; Gaussian model; Generalized Pareto distributions; Hüsler–Reiss triangular arrays; Linear discriminant functions; Mathematical models; Normal distribution; Pareto optimum; Studies; Truncation; secondary; Discriminant analysis; Gaussian model; Linear discriminant functions; Hüsler–Reiss triangular arrays; primary; Truncation; Generalized Pareto distributions
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2011.06.012

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. ► We base classification in discriminant analysis on exceedances above high thresholds. ► Statistical modeling is done with truncated parametric distributions. ► We replace truncated Gaussian distributions by generalized Pareto distributions. ► Properties and relationships of discriminant functions in both models are explored.