Nonparametric estimation of the tree structure of a nested Archimedean copula

TL;DR

This paper introduces a nonparametric, rank-based method for estimating the hierarchical tree structure of nested Archimedean copulas, leveraging trivariate substructure comparisons to avoid parametric assumptions.

Contribution

It proposes a novel nonparametric approach that estimates the tree structure of nested Archimedean copulas using only rank-based methods and trivariate comparisons.

Findings

Accurately estimates tree structures without parametric assumptions

Uses simple pairwise comparisons for structure inference

Applicable to high-dimensional nested copulas

Abstract

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.