Definition: A sufficient statistic is as follows: Suppose one has samples from a distribution, does not know exactly what that distribution is, but does know that it comes from a certain set of distributions that is determined partly or wholly by a certain parameter, q. A statistic is sufficient for
inference about q if and only if the values of any sample from that distribution give no
more information about q than does the value of the statistic on that sample.
E.g. if we know that a distribution is normal with variance 1 but has an unknown mean, the sample average is a sufficient statistic for the mean.
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