The Family of Ancillary Statistics

Though the marginal distributions of the ancillary statistics are independent of the parameter they are not useless or informationless. A set of ancillaries may sometimes summarise the whole of the information contained in the sample. A classification of the ancillaries in terms of the partial order of their information content is attempted here. In general there are many maximal ancillaries, Among the minimal ancillaries there exists a unique largest one. When there exists a complete sufficient statistic, the problem of tracking down the maximal and minimal ancillaries becomes greatly simplified.