Dependence Structures and Linear Transformations. A New Perspective on the Law of Convergence of Types

C. Matrán Bea, L. Trapote Reglero

Skorohod’s representation theorem for convergence in distribution allows for an elementary proof of the Law of Convergence of Types for univariate distributions. We will revisit the Law of Convergence of Types in the multivariate case, based on Billingsley’s original proof and the corresponding Skorohod representation, which significantly simplifies its development. Finally, we will address, with a similar approach, a "law of convergence of dependence structures."

Palabras clave: Law of Convergence of Types depence structure copula Skorohod’s representation theorem

J. Saperas Riera, G. Mateu Figueras, J. A. Martín Fernández

E. Frutos Bernal, E. Ceulemans, P. Galindo-Villardón, T. Wilderjans

G. Mateu-Figueras, G. S. Monti, V. Pawlowsky-Glahn, J. J. Egozcue

J. Palarea-Albaladejo, N. Štefelová, J. A. Martín-Fernández

E. Carrizosa, A. Navas-Orozco