Editing Sufficient statistic (section)

{{Short description|Statistical principle}}
In [[statistics]], '''sufficiency''' is a property of a [[statistic]] computed on a [[Sample (statistics)|sample dataset]] in relation to a parametric model of the dataset. A sufficient statistic contains all of the information that the dataset provides about the model parameters. It is closely related to the concepts of an [[ancillary statistic]] which contains no information about the model parameters, and of a [[complete statistic]] which only contains information about the parameters and no ancillary information.

A related concept is that of '''linear sufficiency''', which is weaker than ''sufficiency'' but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators.<ref>Dodge, Y. (2003) — entry for linear sufficiency</ref> The [[Kolmogorov structure function]] deals with individual finite data; the related notion there is the algorithmic sufficient statistic.

The concept is due to [[Ronald Fisher|Sir Ronald Fisher]] in 1920.<ref name="Fisher19222">{{cite journal |last=Fisher |first=R.A. |author-link=Ronald Fisher |year=1922 |title=On the mathematical foundations of theoretical statistics |url=http://digital.library.adelaide.edu.au/dspace/handle/2440/15172 |journal=Philosophical Transactions of the Royal Society A |volume=222 |issue=594–604 |pages=309–368 |bibcode=1922RSPTA.222..309F |doi=10.1098/rsta.1922.0009 |jfm=48.1280.02 |jstor=91208 |doi-access=free |hdl-access=free |hdl=2440/15172}}</ref> [[Stephen Stigler]] noted in 1973 that the concept of sufficiency had fallen out of favor in [[descriptive statistics]] because of the strong dependence on an assumption of the distributional form (see [[Sufficient statistic#Exponential family|Pitman–Koopman–Darmois theorem]] below), but remained very important in theoretical work.<ref name="Stigler19732">{{cite journal |last=Stigler |first=Stephen |author-link=Stephen Stigler |date=December 1973 |title=Studies in the History of Probability and Statistics. XXXII: Laplace, Fisher and the Discovery of the Concept of Sufficiency |journal=Biometrika |volume=60 |issue=3 |pages=439–445 |doi=10.1093/biomet/60.3.439 |jstor=2334992 |mr=0326872}}</ref>