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Classification into Kullback–Leibler balls in exponential families

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  • Katzur, Alexander
  • Kamps, Udo

Abstract

A classification procedure for a two-class problem is introduced and analyzed, where the classes of probability density functions within a regular exponential family are represented by left-sided Kullback–Leibler balls of natural parameter vectors. If the class membership is known for a finite number of densities, only, classes are defined by constructing minimal enclosing left-sided Kullback–Leibler balls, which are seen to uniquely exist. A connection to Chernoff information between distributions is pointed out.

Suggested Citation

  • Katzur, Alexander & Kamps, Udo, 2016. "Classification into Kullback–Leibler balls in exponential families," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 75-90.
    • Handle: RePEc:eee:jmvana:v:150:y:2016:i:c:p:75-90
    DOI: 10.1016/j.jmva.2016.05.007
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    References listed on IDEAS

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    1. Vuong, Q.N. & Bedbur, S. & Kamps, U., 2013. "Distances between models of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 24-36.
    2. Taniguchi, M., 1994. "Higher Order Asymptotic Theory for Discriminant Analysis in Exponential Families of Distributions," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 169-187, February.
    3. Fischer, Aurélie, 2010. "Quantization and clustering with Bregman divergences," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2207-2221, October.
    4. Koutras, Markos, 1992. "Minimum distance discrimination rules and success rates for elliptical normal mixtures," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 259-268, March.
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    Cited by:

    1. Alexander Katzur & Udo Kamps, 2020. "Classification using sequential order statistics," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 201-230, March.

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