IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v103y2012i1p107-115.html
   My bibliography  Save this article

Some notes on extremal discriminant analysis

Author

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

Abstract

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X11001357
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:107-115. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.