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Some notes on extremal discriminant analysis


  • Manjunath, B.G.
  • Frick, Melanie
  • Reiss, Rolf-Dieter


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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  • Manjunath, B.G. & Frick, Melanie & Reiss, Rolf-Dieter, 2012. "Some notes on extremal discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 107-115, January.
  • Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:107-115

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    References listed on IDEAS

    1. Hashorva, Enkelejd, 2006. "On the multivariate Hüsler-Reiss distribution attracting the maxima of elliptical triangular arrays," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 2027-2035, December.
    2. Hashorva, Enkelejd, 2005. "Elliptical triangular arrays in the max-domain of attraction of Hüsler-Reiss distribution," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 125-135, April.
    3. Robert B. Avery, 1981. "Credit scoring models with discriminant analysis and truncated samples," Research Papers in Banking and Financial Economics 54, Board of Governors of the Federal Reserve System (U.S.).
    4. Frick, Melanie & Reiss, Rolf-Dieter, 2010. "Limiting distributions of maxima under triangular schemes," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2346-2357, November.
    5. Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
    6. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
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    Cited by:

    1. Hashorva, Enkelejd & Peng, Liang & Weng, Zhichao, 2015. "Maxima of a triangular array of multivariate Gaussian sequence," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 62-72.
    2. Hashorva, Enkelejd & Weng, Zhichao, 2013. "Limit laws for extremes of dependent stationary Gaussian arrays," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 320-330.
    3. Michael Asamoah-Boaheng & Atinuke Adebanji & Morire Labeodan, 2016. "Some zero mean classification functions with unequal prior probabilities and non-normality," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 5(3), pages 2.


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