Statistical inference from set-valued observations

Consider a random experiment whose true (unknown) outcome is modelled by a certain randomelementX and the available imprecise observations are modelled by some random set A such that X ∈ A almost surely. The purpose of the paper is to propose a statistical procedure for estimation of the real distribution of X. The asymptotic properties of the suggested procedure are then investigated in both nonparametric and parametric settings. So far, only the results for a finite sample space are available.