Characterizing M-estimators

• 成果类型: Article
• 署名作者: Dimitriadis, Timo; Fissler, Tobias; Ziegel, Johanna
• 署名单位: Ruprecht Karls University Heidelberg; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Bern
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad026
• 发表日期: 2024
• 页码: 339346
• 关键词: EXPECTED SHORTFALL; regression; probabilities; models

摘要

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 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.