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年代提出了基准概念，作为贝叶斯后验分布的潜在替代方案。在过去一个世纪中，基准方法已在各种参数和非参数设定中得到探索。然而，据我们所知，半参数统计领域尚未发展出基准推断方法。本文针对半参数模型提出了一种新颖的基准方法。为简化表述，我们以生存数据分析中最流行的Cox比例风险模型作为贯穿全文的示例，同时讨论了其他模型及扩展。实验结果表明，我们的方法在最大似然估计失效的情况下表现尤为优异。