Discussion of ‘Nonparametric generalized fiducial inference for survival functions under censoring’
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《删失下生存函数的非参数广义 fiducial 推断》讨论
- 研究问题
- 这篇讨论文如何评价广义 fiducial 方法在右删失生存函数推断中的一般特点，以及被讨论主论文所述的渐近推断依据？
- 方法与思路
- 所给文本先概述主论文的生存函数 fiducial 分布和 Bernstein–von Mises 结果，再说明讨论将聚焦该方法的一般特征。
- 材料陈述的贡献
- 讨论文本转述主论文的高斯过程极限及渐近频率误差控制，并介绍其性能比较主张；片段没有展示讨论者自己的完整论证。
- 阅读关注点
- 应区分讨论者评价与主论文定理，核对主论文的删失及正则条件，并阅读讨论后续对 fiducial 方法一般性质的分析。
- 阅读边界
- 所给资料为版本未注明的 OpenAlex 索引讨论文本，不能冒充主论文；转述的理论及性能主张均未在此得到独立核验。
原文摘要
It is a pleasure to participate in the discussion of the article by Cui & Hannig (2019). The authors are to be congratulated for their efforts and ingenuity in developing what is, to my knowledge, the first fiducial solution to a problem involving an infinite-dimensional parameter of interest. Specifically, the authors build on some existing machinery, summarized recently in Hannig et al. (2016) and the references therein, to construct a generalized fiducial distribution for the full event time survival function, |$S$|, in the presence of right censoring. They proceed to show that the generalized fiducial distribution satisfies a Bernstein–von Mises theorem, that is, it asymptotically resembles a Gaussian process centred at the Kaplan–Meier estimator, |$\hat S$|, with covariance function matching that of the limiting sampling distribution of |$\hat S$|. This implies that summaries of the generalized fiducial distribution, such as hypothesis testing rules and confidence sets for |$S$|, will control the frequentist error rates at the nominal level, asymptotically. With theoretical justification in hand, they go on to demonstrate that the methods derived from their generalized fiducial distribution perform as well as or better than state-of-the-art methods in survival analysis. Here I will focus mainly on general features of the generalized fiducial approach, leaving the specific results in survival analysis for the experts to discuss.