Ancillary Statistic

An Ancillary Statistic is a statistic ([math]\displaystyle{ t=T(X) }[/math]) where the sampling distribution ([math]\displaystyle{ X=\{X_1,X_2,..., X_N\} }[/math]) is not dependent on the population parameters ([math]\displaystyle{ \theta }[/math]'s).

See: Sufficient Statistic, Statistic, Sufficiency Principle Likelihood Principle, Conditionality Principle, Birnbaum’s Theorem.

References

(Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Conditionality_principle Retrieved 2016-07-30
- In statistics, an ancillary statistic is a statistic whose sampling distribution does not depend on the parameters of the model. An ancillary statistic is a pivotal quantity that is also a statistic. Ancillary statistics can be used to construct prediction intervals.
  This concept was introduced by the statistical geneticist Sir Ronald Fisher.

(Cox, 2006) ⇒ David R. Cox. (2006). “Principles of Statistical Inference.” Cambridge University Press. ISBN:9780521685672

(Kalbfleisch,1975) ⇒ Kalbfleisch, J. D. (1975). Sufficiency and conditionality. Biometrika, 62(2), 251-259. DOI: 10.1093/biomet/62.2.251 [1]
- Ancillary statistics are divided into two logically distinct types: those determined by the experimental design and those determined by the mathematical modelling of the problem. It is pointed out that, in the class of inference problems where our purpose is to gain information or insight into the nature of a chance set-up, a weakened conditionality principle when applied first removes the possibility of deriving the likelihood principle. Since to some extent a conditionality principle must be applied in experiment definition, it is argued that this is a necessary first step if full acceptance of the likelihood axiom is to be avoided.