The James–Stein estimator is a biased estimator of the mean, , of (possibly) correlated Gaussian distributed random vectors with unknown means . It arose sequentially in two main published papers, the earlier version of the estimator was developed by Charles Stein in 1956, which reached a relatively shocking conclusion that while the then usual estimate of the mean, or the sample mean written by Stein and James as , is admissible when , however it is inadmissible when and proposed a possible improvement to the estimator that shrinks the sample means towards a more central mean vector (which can be chosen a priori or commonly the "average of averages" of the sample means given all samples share the same size), is commonly referred to as Stein's example or paradox. This earlier result wa