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Characterizing M-estimators

Author

Listed:
  • Timo Dimitriadis Alfred Weber
  • Tobias FisslerRiskLab
  • Johanna Ziegel

Abstract

SummaryWe characterize the full classes of M-estimators for semiparametric models of general functionals by formally connecting the theory of consistent loss functions from forecast evaluation with the theory of M-estimation. This novel characterization result allows us to leverage existing results on loss functions known from the literature on forecast evaluation in estimation theory. We exemplify advantageous implications for the fields of robust, efficient, equivariant and Pareto-optimal M-estimation.

Suggested Citation

  • Timo Dimitriadis Alfred Weber & Tobias FisslerRiskLab & Johanna Ziegel, 2024. "Characterizing M-estimators," Biometrika, Biometrika Trust, vol. 111(1), pages 339-346.
    • Handle: RePEc:oup:biomet:v:111:y:2024:i:1:p:339-346.
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