Admissible estimator

An estimator is admissible when no other estimator has risk no larger at every parameter value and strictly smaller at at least one value.

For one observation $X\sim N_p(\theta ,I_p)$ with $p\ge 3$, the James–Stein estimator isUnder quadratic loss, Stein's risk identity givesso it dominates the usual estimator $X$.

The James-Stein risk is strictly below the dimension at every finite parameter, but its improvement tends to zero as the mean norm tends to infinity. Strict pointwise domination therefore leaves the supremum risk unchanged.