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Fiducial Inference, introduced by Fisher in the 1930s, has a long history,which at times aroused passionate disagreements. However, its application hasbeen largely confined to relatively simple parametric problems. In this paper,we present what might be the first time fiducial inference, as generalized byHannig et al. (2016), is systematically applied to estimation of anonparametric survival function under right censoring. We find that theresulting fiducial distribution gives rise to surprisingly good statisticalprocedures applicable to both one sample and two sample problems. Inparticular, we use the fiducial distribution of a survival function toconstruct pointwise and curvewise confidence intervals for the survivalfunction, and propose tests based on the curvewise confidence interval. Weestablish a functional Bernstein-von Mises theorem, and perform thoroughsimulation studies in scenarios with different levels of censoring. Theproposed fiducial based confidence intervals maintain coverage in situationswhere asymptotic methods often have substantial coverage problems. Furthermore,the average length of the proposed confidence intervals is often shorter thanthe length of competing methods that maintain coverage. Finally, the proposedfiducial test is more powerful than various types of log-rank tests and suplog-rank tests in some scenarios. We illustrate the proposed fiducial testcomparing chemotherapy against chemotherapy combined with radiotherapy usingdata from the treatment of locally unresectable gastric cancer.

Nonparametric generalized fiducial inference for survival functions under censoring