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:
“A healthy man, indeed, is the complement of the seasons, and in winter, summer is in his heart.”
—Henry David Thoreau (1817–1862)