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

Authors: J. Górecki, Martin Holeňa
Publication year: 2014
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: New Frontiers in Mining Complex Patterns
Projects: Constructing Advanced Comprehensible Classifiers
Bibliographic citation: GÓRECKI, J., HOLEŇA, Martin. 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.W., eds. New Frontiers in Mining Complex Patterns. Cham: Springer, 2014, S. 132-147. Lecture Notes in Artificial Intelligence, 8399. ISBN 978-3-319-08406-0. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-319-08407-7_9
DOI: 10.1007/978-3-319-08407-7_9
ID: 430472

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.