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arXiv · 2208.08108

Characterizing M-estimators

Timo Dimitriadis·Tobias Fissler·Johanna Ziegel
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Abstract

We 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 opens up the possibility for theoretical research on efficient and equivariant M-estimation and, more generally, it allows to leverage existing results on loss functions known from the literature of forecast evaluation in estimation theory.

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Timo Dimitriadis, Tobias Fissler, Johanna Ziegel. 2022-08-17. Characterizing M-estimators. https://doi.org/10.1093/biomet%2Fasad026

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