Sufficient statistic

In statistics, sufficiency is a property of a statistic computed on a 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.^[1] The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic.

The concept is due to Sir Ronald Fisher in 1920.^[2] 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 Pitman–Koopman–Darmois theorem below), but remained very important in theoretical work.^[3]