Barczy Mátyás: Axiomatic characterisation of generalized Psi-estimators

We introduce the notion of generalized Psi-estimators as unique points of sign change of some appropriate functions.
This notion is a generalization of usual Psi-estimators (also called Z-estimators).
We give necessary as well as sufficient conditions for the (unique) existence of generalized Psi-estimators.
Furthermore, we obtain axiomatic characterisations of generalized Psi-estimators and (usual) Psi-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.
This is a joint work with Zsolt Páles.