Nested Archimedean copulas: a new class of nonparametric tree structure estimators

TL;DR

This paper introduces a new nonparametric class of estimators for nested Archimedean copulas based on phylogenetic tree structures, demonstrating improved speed and performance through simulations and real data applications.

Contribution

A novel two-step nonparametric estimator for nested Archimedean copulas that constructs and collapses binary trees, outperforming existing methods in speed and accuracy.

Findings

New estimators are faster than existing methods.

The estimators generally provide better performance in simulations.

Applied estimator yields meaningful insights on real datasets.

Abstract

Any nested Archimedean copula is defined starting from a rooted phylogenetic tree, for which a new class of nonparametric estimators is presented. An estimator from this new class relies on a two-step procedure where first a binary tree is built and second is collapsed if necessary to give an estimate of the target tree structure. Several examples of estimators from this class are given and the performance of each of these estimators, as well as of the only known comparable estimator, is assessed by means of a simulation study involving target structures in various dimensions, showing that the new estimators, besides being faster, usually offer better performance as well. Further, among the given examples of estimators from the new class, one of the best performing one is applied on three datasets: 482 students and their results to various examens, 26 European countries in 1979 and the percentage of workers employed in different economic activities, and 104 countries in 2002 for which various health-related variables are available. The resulting estimated trees offer valuable insights on the analyzed data. The future of nested Archimedean copulas in general is also discussed.