R. A. Fisher introduced the fiducial distribution as a potential replacement for the Bayesian posterior distribution in the 1930s. During the past century, fiducial approaches have been explored in various parametric and nonparametric settings. However, to the best of our knowledge, no fiducial inference has been developed in the realm of semiparametric statistics. In this paper, we propose a novel fiducial approach for semiparametric models. In memory of Sir David Cox who passed away in 2022, we use the Cox proportional hazards model, which is the most popular model for the analysis of survival data, as a running example. Other models and extensions are also discussed. In our experiments, we find that our method performs particularly well in situations where the maximum likelihood estimator fails.

翻译：R. A. Fisher于20世纪30年代提出置信分布作为贝叶斯后验分布的潜在替代方案。在过去一个世纪中，置信方法已在多种参数和非参数情境下得到探索。然而，据我们所知，在半参数统计领域尚未发展出置信推断方法。本文针对半参数模型提出一种新型置信方法。为纪念2022年逝世的David Cox爵士，我们以生存数据分析中最常用的Cox比例风险模型作为贯穿性案例展开讨论，同时涵盖其他模型及推广形式。实验表明，本方法在极大似然估计失效的情境下表现尤为出色。