Estimators for Archimedean copulas in high dimensions

Abstract

The performance of known and new parametric estimators for Archimedean copulas is investigated, with special focus on large dimensions and numerical difficulties. In particular, method-of-moments-like estimators based on pairwise Kendall's tau, a multivariate extension of Blomqvist's beta, minimum distance estimators, the maximum-likelihood estimator, a simulated maximum-likelihood estimator, and a maximum-likelihood estimator based on the copula diagonal are studied. Their performance is compared in a large-scale simulation study both under known and unknown margins (pseudo-observations), in small and high dimensions, under small and large dependencies, various different Archimedean families and sample sizes. High dimensions up to one hundred are considered for the first time and computational problems arising from such large dimensions are addressed in detail. All methods are implemented in the open source \R{} package \pkg{copula} and can thus be easily accessed and studied.