Given a statistic T that is not sufficient, an ancillary complement is a statistic U that is ancillary to T and such that (T, U) is sufficient. Intuitively, an ancillary complement "adds the missing information" (without duplicating any).
The statistic is particularly useful if one takes T to be a maximum likelihood estimator, which in general will not be sufficient; then one can ask for an ancillary complement. In this case, Fisher argues that one must condition on an ancillary complement to determine information content: one should consider the Fisher information content of T to not be the marginal of T, but the conditional distribution of T, given U: how much information does T add? This is not possible in general, as no ancillary complement need exist, and if one exists, it need not be unique, nor does a maximum ancillary complement exist.
Read more about this topic: Ancillary Statistic
Famous quotes containing the word complement:
“There may be as much nobility in being last as in being first, because the two positions are equally necessary in the world, the one to complement the other.”
—José Ortega Y Gasset (1883–1955)