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Sufficient Statistics

bactra.org · 2,094 words · saved by 1 readers

In statistical theory, a "statistic" is a well-behaved (i.e., "measurable") function of the data, which is what's actually used in calculations or inferences, rather than the full data set. E.g., the sample mean, the sample median, the sample variance, etc. A statistic is sufficient if it is just as informative as the full data. The concept was introduced by R. A. Fisher in the 1920s, and refined by Jerzy Neyman in the 1930s. Parametric sufficiency means that the statistic contains just as much information about (some) parameter of the model as the full data. More precisely: the actual data has a certain probability distribution conditional on the data, which in general will also involve the parameter. The statistic is sufficient if this conditional distribution is the same for all parameter values. (That's actually clearer in algebra but I don't feel up to writing it in HTML now.) Once we've controlled for the sufficient statistic, nothing else --- not even the original data --- can t

Sufficient Statistics Notebooks Sufficient Statistics Last update : 13 Apr 2026 12:57 First version : 17 November 2005; expanded with actual math 8 April 2026 \[ \newcommand{\Prob}[1]{\mathbb{P}\left( #1 \right)} \newcommand{\Indicator}[1]{\mathbb{1}\left( #1 \right)} \] In statistical theory, a "statistic" is a well-behaved (i.e., "measurable") function of the data, which is what's actually used in calculations or inferences, rather than the full data set. E.g., the sample mean, the sample median, the sample variance, etc. A statistic is sufficient if it is just as informative as the full dat

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