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Sufficient statistic
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<p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, sufficiency is a property of a <a href="/facts/Statistic/av21WaMK">statistic</a> computed on a <a href="/facts/Sample_(statistics)/URCwKNge">sample dataset</a> 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 <a href="/facts/Ancillary_statistic/67RmgpJN">ancillary statistic</a> which contains no information about the model parameters, and of a <a href="/facts/Complete_statistic/pkF2PzCL">complete statistic</a> which only contains information about the parameters and no ancillary information. </p><p>A related concept is that of linear sufficiency, which is weaker than <i>sufficiency</i> but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The <a href="/facts/Kolmogorov_structure_function/Wo9lWAHk">Kolmogorov structure function</a> deals with individual finite data; the related notion there is the algorithmic sufficient statistic. </p><p>The concept is due to <a href="/facts/Ronald_Fisher/I2FVIpy9">Sir Ronald Fisher</a> in 1920. <a href="/facts/Stephen_Stigler/VyCKqbS6">Stephen Stigler</a> noted in 1973 that the concept of sufficiency had fallen out of favor in <a href="/facts/Descriptive_statistics/vnTP8Ryr">descriptive statistics</a> 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. </p>