Summary
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.
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References
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Acknowledgement
I Wish to thank Dr. R. R. Bahadur for some useful discussions.
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Basu, D. (2011). The Family of Ancillary Statistics. In: DasGupta, A. (eds) Selected Works of Debabrata Basu. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5825-9_18
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