Abstract We give axiomatic characterisations of generalized ψ -estimators and (usual) ψ -estimators (also called Z -estimators), respectively. The key properties of estimators that come into play in the characterisation theorems are the symmetry, the (strong) internality and the asymptotic idempotency. In the proofs, a separation theorem for Abelian subsemigroups plays a crucial role.
Barczy et al. (Sat,) studied this question.