R. A. Fisher introduced the concept of fiducial 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. To streamline our presentation, 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 our method to perform well especially in situations when the maximum likelihood estimator fails.

翻译：R. A. Fisher于20世纪30年代提出了可信推断的概念，作为贝叶斯后验分布的潜在替代方案。在过去的一个世纪中，可信方法已在各种参数和非参数设定下得到探索。然而，据我们所知，在非参数统计领域尚未发展出可信推断方法。本文针对半参数模型提出了一种新的可信方法。为简化表述，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示例，并讨论了其他模型及其扩展。实验表明，我们的方法在最大似然估计失效的情形下表现尤为出色。