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Structure Determination and Estimation of Hierarchical Archimedean Copulas Based on Kendall Correlation Matrix

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New Frontiers in Mining Complex Patterns (NFMCP 2013)

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Abstract

An estimation method for the copula of a continuous multivariate distribution is proposed. A popular class of copulas, namely the class of hierarchical Archimedean copulas, is considered. The proposed method is based on the close relationship of the copula structure and the values of Kendall’s tau computed on all its bivariate margins. A generalized measure based on Kendall’s tau adapted for purposes of the estimation is introduced. A simple algorithm implementing the method is provided and its effectiveness is shown in several experiments including its comparison to other available methods. The results show that the proposed method can be regarded as a suitable alternative to existing methods in the terms of goodness of fit and computational efficiency.

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Notes

  1. 1.

    Sometimes called fully-nested Archimedean copula.

  2. 2.

    Sometimes called partially-nested Archimedean copula.

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Acknowledgment

The research reported in this paper has been supported by the Czech Science Foundation (GA ČR) grant 13-17187S.

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Authors and Affiliations

  1. Department of Informatics, SBA in Karvina, Silesian University in Opava, Karvina, Czech Republic

    Jan Górecki

  2. Institute of Computer Science, Academy of Sciences of the Czech Republic, Praha, Czech Republic

    Martin Holeňa

Authors
  1. Jan Górecki
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  2. Martin Holeňa
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Corresponding author

Correspondence to Jan Górecki .

Editor information

Editors and Affiliations

  1. Università degli Studi di Bari Aldo Moro, Bari, Italy

    Annalisa Appice

  2. Università degli Studi di Bari Aldo Moro, Bari, Italy

    Michelangelo Ceci

  3. Università degli Studi di Bari Aldo Moro, Bari, Italy

    Corrado Loglisci

  4. ICAR, CNR, Rende, Italy

    Giuseppe Manco

  5. Rende, Italy

    Elio Masciari

  6. Department of Computer Science, University of North Carolina, Charlotte, North Carolina, USA

    Zbigniew W. Ras

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Górecki, J., Holeňa, M. (2014). Structure Determination and Estimation of Hierarchical Archimedean Copulas Based on Kendall Correlation Matrix. In: Appice, A., Ceci, M., Loglisci, C., Manco, G., Masciari, E., Ras, Z. (eds) New Frontiers in Mining Complex Patterns. NFMCP 2013. Lecture Notes in Computer Science(), vol 8399. Springer, Cham. https://doi.org/10.1007/978-3-319-08407-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-08407-7_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08406-0

  • Online ISBN: 978-3-319-08407-7

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