Xi'an's Og

While the classical definition of a statistic is one of a real valued random variable or vector, less usual situations call for broader definitions… For instance, in an homework problem from Mark Schervish’s Theory of Statistics, a sample from the uniform distribution of a ball of unknown centre θ and radius ς is associated with the convex hull of said sample as “sufficient statistic”, albeit the object being a set. Similarly, if the radius ς is known, the set made of the intersection of all the balls of radius ς centred at the observations is sufficient, in that the likelihood is constant for θ inside and zero outside. As discussed in this X validated question, this does not define an optimal estimator of the center θ, while Pitman’s best location equivariant does, while the centre of this sufficient set, but it is not sufficient as a statistic and is not necessarily the MVUE, if unbiased.

This entry was posted on June 18, 2022 at 12:22 am and is filed under Books, Kids, Statistics with tags best unbiased estimator, cross validated, sufficiency, sufficient statistics, theory of statistics, UMVUE, uniform distribution. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.