  One of the features inherent in nested Archimedean copulas, also called
hierarchical Archimedean copulas, is their rooted tree structure. A
nonparametric, rank-based method to estimate this structure is presented. The
idea is to represent the target structure as a set of trivariate structures,
each of which can be estimated individually with ease. Indeed, for any three
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 margins of the empirical distribution of the three variables. The set
of estimated trivariate structures can then be used to build an estimate of the
target structure. The advantage of this estimation method is that it does not
require any parametric assumptions concerning the generator functions at the
nodes of the tree.
