On the validation of fiducial techniques

A structured model is essentially a family of random vectors X θ defined on a probability space with values in a sample space. If, for a given sample value x and for each ω in the probability space, there is at most one parameter value θ for which X θ (ω) is equal to x , then the model is called additive at x. When a certain conditional distribution exists, a frequency interpretation specific to additive structured models holds, and is summarized in a unique structured distribution for the parameter. Many of the techniques used by Fisher in deriving and handling his fiducial probability distribution are shown to be valid when dealing with a structured distribution.