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.
Sometimes called fully-nested Archimedean copula.
- 2.
Sometimes called partially-nested Archimedean copula.
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The research reported in this paper has been supported by the Czech Science Foundation (GA ČR) grant 13-17187S.
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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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