  The presence of multiparticle entanglement is an important benchmark for the
performance of intermediate-scale quantum technologies. In this work we
consider statistical methods based on locally randomized measurements in order
to characterize different degrees of multiparticle entanglement in qubit
systems. We introduce hierarchies of criteria, satisfied by states which are
separable with respect to partitions of different size, involving only second
moments of the underlying probability distribution. Furthermore, we study in
detail the resources required for a statistical estimation of the respective
moments if only a finite number of samples is available, and discuss their
scaling with the system size.
