Approximations of copulas and relative distribution functions via transformed moments: Some applications

In this talk we introduce several procedures of recovering the copulas, regression and density of relative distribution given the sequence of transformed moments. The uniform convergence of copula as well as the uniform rate for approximates of copula density function are established. Questions about approximating the Radon transform inverse are discussed as well. It is shown how the rate of approximations are related to the number of transformed moments. Asymptotic behavior of proposed approximations and their empirical counterparts are illustrated by means of a simulation study.