Building on the recent development of the model-free generalized fiducial (MFGF) paradigm (Williams, 2023) for predictive inference with finite-sample frequentist validity guarantees, in this paper, we develop an MFGF-based approach to decision theory. Beyond the utility of the new tools we contribute to the field of decision theory, our work establishes a formal connection between decision theories from the perspectives of fiducial inference, conformal prediction, and imprecise probability theory. In our paper, we establish pointwise and uniform consistency of an {\em MFGF upper risk function} as an approximation to the true risk function via the derivation of nonasymptotic concentration bounds, and our work serves as the foundation for future investigations of the properties of the MFGF upper risk from the perspective of new decision-theoretic, finite-sample validity criterion, as in Martin (2021).

翻译：基于无模型广义可信推断（MFGF）范式（Williams, 2023）在具有有限样本频率学派有效性保证的预测推断方面的最新进展，本文提出了一种基于MFGF的决策理论方法。除了为决策理论领域贡献新工具外，我们的工作还建立了从可信推断、共形预测和精确概率理论角度出发的决策理论之间的形式化联系。在论文中，我们通过推导非渐近浓度界，证明了作为真实风险函数近似的MFGF上风险函数的逐点一致性和一致一致性，这为基于Martin（2021）提出的新决策理论有限样本有效性准则研究MFGF上风险函数性质奠定了未来探索基础。