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<p>We give axiomatic characterisations of generalized <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-estimators and (usual) <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-estimators (also called <i>Z</i>-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.</p>

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Axiomatic characterisation of generalized \({\psi }\)-estimators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月18日

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  • Mátyás Barczy,
  • Zsolt Páles

摘要

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