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Axiomatic characterisation of generalized $ψ$-estimators

Matyas Barczy, Zsolt Páles

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.

Axiomatic characterisation of generalized $ψ$-estimators

Abstract

We give axiomatic characterisations of generalized -estimators and (usual) -estimators (also called -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.
Paper Structure (3 sections, 65 equations)

This paper contains 3 sections, 65 equations.

Table of Contents

  1. Introduction
  2. Characterisation theorem for generalized $\psi$-estimators
  3. Characterisation theorem for (usual) $\psi$-estimators