Mathematical Statistics Lesson of the Day – An Example of An Ancillary Statistic

June 26, 2015
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(This article was originally published at The Chemical Statistician » Statistics, and syndicated at StatsBlogs.)

Consider 2 random variables, X_1 and X_2, from the normal distribution \text{Normal}(\mu, \sigma^2), where \mu is unknown.  Then the statistic

D = X_1 - X_2

has the distribution

\text{Normal}(0, 2\sigma^2).

The distribution of D does not depend on \mu, so D is an ancillary statistic for \mu.

Note that, if \sigma^2 is unknown, then D is not ancillary for \sigma^2.


Filed under: Mathematical Statistics, Statistics, Statistics Lesson of the Day Tagged: ancillary statistic, ancillary statistics, estimation, math, mathematical statistics, mathematics, normal distribution, point estimation, random variable, statistics



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