Uyttendaele, Nathan
[UCL]
A lot of progress regarding estimation of nested Archimedean cop- ulas has been booked since their introduction by Joe (1997). The currently published procedures can be seen as particular cases of two different, more general, approaches. In the first approach, the tree structure of the target nested Archimedean copulas is estimated us- ing hierarchical clustering to get a binary tree and then parts of this binary tree are collapsed according to some strategy. This two-step estimation of the tree structure paves the way for an easy estimation of the generators afterwards. In contrast to the first approach, the sec- ond approach estimates the tree structure free of any concern for the generators. While this is the main strength of this second approach, it is also its main weakness: estimation of the generators afterwards still lacks a solution. In this paper, both approaches are formally explored, detailed explanations and examples are given, as well as results from a performance study where a new way of comparing tree structure esti- mators is offered. A nested Archimedean copula is also estimated based on exams results from 482 students, and a naive attempt to check the fit is made using principal component analysis.
| Bibliographic reference |
Uyttendaele, Nathan. On the estimation of nested Archimedean copulas: A theoretical and an experimental comparison. ISBA Discussion Paper ; 2016/05 (2016) 27 pages |
| Permanent URL |
http://hdl.handle.net/2078.1/171500 |
