Mean-vector prediction risk
= Mean-vector prediction risk
{title2=$\mathbb E\|\widehat\mu-\mu\|^2$}
The mean-vector prediction risk measures squared <Euclidean norm> error in estimating the deterministic response mean. For <independent> future noise with <covariance matrix> $\sigma^2I_n$, prediction of a new noisy response adds $n\sigma^2$ to this risk. A Gaussian <orthogonal projection matrix> $P$ of rank $k$ has risk $\|(I-P)\mu\|^2+k\sigma^2$.