A class of closeness criteria

A generalized class of closeness criteria for the pairwise comparison of estimators is defined. This class contains an infinite number of members including Pitman's measure of closeness and at least one transitive criterion. Several specific members of the class are examined, and their relationships to Rao concentration and stochastic domination are shown. Graphical and analytical characterizations are shown for these members of the class. Examples are given which illustrate the behavior of some of these criteria.