Fiducial inference - A Neyman-Pearson interpretation

Fisher's fiducial argument is a tool for deriving inferences in the form of a probability distribution on the parameter space, not based on Bayes's Theorem. Lindley established that in exceptional situations fiducial inferences coincide with posterior distributions; in the other situations fiducial inference has always been critized. In his comment on Wilkinson [1], James wrote 'Fisher's postulate of ignorance for fiducial theory should be replaced by a positive requirement that the statistical analysis is appropriate to and meets the issues at stake.' Such a positive requirement can be obtained from a decision theoretic approach: in some interesting situations procedures provided by the fiducial argument are optimal in a class of risk-unbiased procedures.