Rejoinder: ‘Nonparametric generalized fiducial inference for survival functions under censoring’

Abstract

1. Introduction We are very grateful to Professors Taraldsen, Lindqvist and Martin for providing stimulating and thoughtful discussions about our paper ( Cui & Hannig, 2019). Several important questions are raised by the discussants. We respond to their comments in turn, omitting those points we agree with or to which we have nothing insightful to add. 2. Response to Professors Taraldsen and Lindqvist Thank you for the thorough review of fiducial inference in the first part of your discussion ( Taraldsen & Lindqvist, 2019). An interesting question arises: why was fiducial inference so controversial? While different people will have different opinions, we feel that it has to do with the fact that Fisher (1935) was selling the idea as a unique way to obtain optimal, well-calibrated, posterior-like distributions on the parameter space. It quickly became apparent, as examples of nonuniqueness and poor calibration emerged, that such a goal is impossible to achieve ( Dawid et al., 1973; Hannig, 2013). Additional properties were posited by Fisher and refuted by others; see, for example, Lindley (1958). A natural question is what led Fisher to have such a strong prior in favour of these properties?