Characterizing M-estimators

Timo Dimitriadis; Tobias Fissler; Johanna Ziegel

doi:10.48550/arXiv.2208.08108

Characterizing M-estimators

Timo Dimitriadis, Tobias Fissler, Johanna Ziegel

Institute for Statistics and Mathematics

Publication: Working/Discussion Paper › Working Paper/Preprint

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.

Original language	English
Number of pages	14
DOIs	https://doi.org/10.48550/arXiv.2208.08108
Publication status	Published - 2022

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