Minimax sample mean for a nonnegative normal location
= Minimax sample mean for a nonnegative normal location
For independent $X_i\sim N(\theta,1)$ with $\theta\ge0$, the sample mean has constant squared-error risk $1/n$ and is minimax. Smooth priors supported on $[0,L]$ whose prior Fisher information is $O(L^{-2})$ give, through the <Van Trees inequality>, a lower bound tending to $1/n$ for every rule's worst-case risk.