Nonparametric estimation of marginal distributions for unordered pairs

In this article, we consider the estimation of the marginal distributions for pairs of data are recorded, with unobserved order in each pair. New estimators are proposed and their asymptotic properties are established, by proving a Glivenko-Cantelli theorem and a functional central limit result. Results from a simulation study are included and we illustrate the applicability of the method on the homologous chromosomes data.