Ancillary statistic
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An ancillary statistic is a measure of a sample whose distribution (or whose pmf or pdf) does not depend on the parameters of the model.[1][2][3] An ancillary statistic is a pivotal quantity that is also a statistic. Ancillary statistics can be used to construct prediction intervals. They are also used in connection with Basu's theorem to prove independence between statistics.[4]
This concept was first introduced by Ronald Fisher in the 1920s,[5] but its formal definition was only provided in 1964 by Debabrata Basu.[6][7]