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Axiomatic frameworks characterize generalized psi-estimators, indicating key mathematical properties.
We give axiomatic characterisations of generalized ψ ψ -estimators and (usual) ψ 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.
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Barczy et al. (2026) studied this question.
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