Some Ancillary Statistics and Their Properties

Two lists are given. The first is a list of properties of ancillary statistics; the second is a list of examples of ancillary statistics. It is then indicated which of the properties are satisfied by each example. Many of the models have the property that the parameter θ is a location parameter for the maximum likelihood estimator (MLE) in every conditional distribution determined by a fixed value of the ancillary statistic. In certain other models the same state of affairs is achieved by parameter transformation. In either of these cases we call the ancillary an "exact precision index." There exist irregular models in which the precision of estimation depends not only on the ancillary but on θ as well. Some comments are offered on approximate ancillarity and on the conditionality principle.