摘要：We study the impact of certain transformations within theclass of Archimedean copulas. We give some admissibilityconditions for these transformations, and define some equivalenceclasses for both transformations and generators ofArchimedean copulas. We extend the r-fold composition ofthe diagonal section of a copula, from r ∈ N to r ∈ R. This extension,coupled with results on equivalence classes, gives usnew expressions of transformations and generators. Estimatorsderiving directly from these expressions are proposedand their convergence is investigated. We provide confidencebands for the estimated generators. Numerical illustrationsshow the empirical performance of these estimators.
关键词：Transformations of Archimedean copulas; self-nested diagonal; non-parametric estimation; tail dependence
