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

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