A metric space of subcopulas - An approach via Hausdorff distance

摘要

In this work, we define a distance function on the set of bivariate subcopulas to generate a compact metric space. Moreover, the copula space equipped with the uniform distance is essentially a metric subspace of this subcopula space. We also characterize the convergence in this space, and provide the interrelationship with the convergence of the distribution functions. (C) 2019 Published by Elsevier B.V.