Axiomatic characterisation of generalized $\ddot{I}ˆ$-estimators

Abstract

We give axiomatic characterisations of generalized $\ddot{I}ˆ$-estimators and (usual) $\ddot{I}ˆ$-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.

20 pages