Comparing Location Experiments

Abstract

In Sections 1–3, the classical theory of the comparison of two experiments is reviewed with particular reference to the comparison of two location experiments. It is shown that the requirement of domination of one experiment by another for all decision problems is too strong to provide a reasonable basis for comparison. For one-parameter problems with monotone likelihood ratio, it is therefore proposed to restrict the comparison to decision problems that are monotone in the sense of Karlin and Rubin (1956). Application of this weaker definition to the location problem is shown to give satisfactory results. A scale-free comparison of this type leads to a new tail-ordering of distributions, and this is explored in Section 6.