Set Estimation from Projected Multidimensional Random Variables with Application to a Discrete-Time Skorokhod Problem

This paper deals with sufficient conditions on the distribution of the random variable H, in the model X =ΠC(H), for the convex hull CN of N independent copies of X to be a consistent estimator of the convex body C with a rate of convergence. The convergence of CN is established for the Hausdorff distance under a uniform condition on the distribution of H, but also in a pointwise sense under a less demanding condition. Some of these convergence results on CN are applied to the estimation of the time-dependent constraint set involved in a discrete-time Skorokhod problem.