On partial sufficiency and partial ancillarity

Abstract In connection with a new model for two-way sample schemes with discrete observations introduced by Rasch 11 and 12, the idea of basing the statistical analysis entirely upon conditional distributions was suggested. The main feature of this method of analysis can be summarized as follows. Suppose the given probability distribution is defined on a product parameter space, say Θ × E, and suppose we want to make statistical inference concerning θ ∈ Θ. If there exists a probability distribution which is independent of ε ∈ E and thus only depends on θ ∈ Θ we shall in accordance with Rasch 12 say that statistical inference based on this probability distribution is specific objective with respect to θ. We shall not in this paper discuss the justification of this type of inference or possible implications of the method. We shall mainly discuss the uniqueness of the method and study certain probabilistic characterizations of the probability distributions which contain the specific objective information about each of the two parameters in the product set Θ × E.