We construct two pairs (\A[1]F,\A[2]F) and (\A[1]ψ,\A[2]ψ) of ordered parametric families of symmetric dependence functions. The families of the first pair are indexed by regular distribution functions F, and those of the second pair by elements ψ of a specific function family \bpsi. We also show that all solutions of the differential equation dydu=α(u)u(1−u)y for α in a certain function family \balphas are symmetric dependence functions.
\noindent We introduce new estimates and tests of independence in copula models with unknown margins using ϕ-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior or a boundary value of the parameter space. Simulation results show that the choice of χ2-divergence has good properties in terms of efficiency-robustness.
The aim of this paper is to open a new way of modelling non-exchangeable random variables with a class of Archimax copulas. We investigate a connection between powers of generators and dependence functions, and propose some construction methods for dependence functions. Application to different hydrological data is given.