= Unbiased Gaussian projection risk estimate
{title2=$\|(I-P)Y\|^2+(2k-n)\widehat\sigma^2$}
For $Y\sim N_n(\mu,\sigma^2I)$ and a fixed <orthogonal projection matrix> $P$ of rank $k$, the displayed expression is an <unbiased estimator> of the <mean-vector prediction risk> whenever $\widehat\sigma^2$ is an <unbiased estimator> of $\sigma^2$. <Independence> of its two terms is unnecessary. Comparing fixed models yields the <Mallows Cp> penalty, but minimizing unbiased estimates does not preserve unbiasedness after selection.
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