James–Stein estimator

The James–Stein estimator is a biased estimator of the mean of Gaussian random vectors. It can be shown that the James–Stein estimator dominates the "ordinary" least squares approach, i.e., it has lower mean squared error. It is the best-known example of Stein's phenomenon.

An earlier version of the estimator was developed by Charles Stein in 1956, and is sometimes referred to as Stein's estimator. The result was improved by Willard James and Charles Stein in 1961.

Suppose the vector ${\displaystyle {\boldsymbol {\theta }}}$ is the unknown mean of a ${\displaystyle m}$-variate normally distributed (with known covariance matrix ${\displaystyle \sigma ^{2}I}$) random variable ${\displaystyle {\mathbf {Y} }}$:

...
Wikipedia