  We analyze statistical properties of plug-in estimators for unbalanced
optimal transport quantities between finitely supported measures in different
prototypical sampling models. Specifically, our main results provide
non-asymptotic bounds on the expected error of empirical Kantorovich-Rubinstein
(KR) distance, plans, and barycenters for mass penalty parameter $C>0$. The
impact of the mass penalty parameter $C$ is studied in detail. Based on this
analysis, we mathematically justify randomized computational schemes for KR
quantities which can be used for fast approximate computations in combination
with any exact solver. Using synthetic and real datasets, we empirically
analyze the behavior of the expected errors in simulation studies and
illustrate the validity of our theoretical bounds.
