Axiomatic characterisation of generalized $\psi$-estimators

TL;DR

This paper provides axiomatic characterizations of generalized and usual $oldsymbol{ extpsi}$-estimators, highlighting key properties like symmetry, internality, and asymptotic idempotency, with a crucial use of a separation theorem for Abelian subsemigroups.

Contribution

It introduces axiomatic characterizations of $oldsymbol{ extpsi}$-estimators, expanding understanding of their fundamental properties and mathematical structure.

Findings

Key properties include symmetry, internality, and asymptotic idempotency.

Separation theorem for Abelian subsemigroups is crucial in proofs.

Provides a foundational framework for understanding $oldsymbol{ extpsi}$-estimators.

Abstract

We give axiomatic characterisations of generalized $\psi$-estimators and (usual) $\psi$-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.