Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution

摘要: Abstract : If one observes the real random variables Xi, Xn independently normally distributed with unknown means xi...x in and variance 1, it is customary to estimate xi by Xi. loss sum of squares errors, this estimator admissible for n or equal 2, but inadmissible more than 3. Since usual best among those which transform correctly under translation, any equals 3 involves an arbitrary choice. While results paper are not a form suitable immediate practical application, possible improvement over seems be large enough importance if large.