Nonparametric estimation of the tree structure of a nested Archimedean copula
(2013) , 25 pages
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- Abstract
- One of the features inherent in nested Archimedean copulas, also called hier- archical Archimedean copulas, is their rooted tree structure. In this paper, a nonparametric, rank-based method to estimate this structure is developed. Our approach consists in representing the rooted tree structure as a set of trivariate structures that can be estimated individually. Indeed, for any triple of variables there are only four possible rooted tree structures and, based on a sample, a choice can be made by performing comparisons between the three bivariate mar- gins of the empirical distribution of the triple. The set of estimated trivariate structures can then be used to build an estimate of the global rooted tree struc- ture. This approach has the advantage that no assumptions about the nested Archimedean copula is required prior to the estimation of its structure.
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Citations
Segers, J., & Uyttendaele, N. (2013). Nonparametric estimation of the tree structure of a nested Archimedean copula (ISBA Discussion paper 2013/09). https://hdl.handle.net/2078.5/206734