= Rao-Blackwell estimator after interim selection
{c}
{title2=$\widetilde\delta=S-v\lambda((c-S)/v)$}
For two independent stage means $X,Y\sim N(\delta,s^2)$ and continuation $X\ge c$, let $S=(X+Y)/2$ and $v=s/\sqrt2$. The second-stage mean is conditionally unbiased. The <Rao-Blackwell theorem> gives $E(Y\mid S,X\ge c)=S-v\lambda((c-S)/v)$, using $X\mid S\sim N(S,v^2)$ and truncation. This is a <conditionally unbiased estimator> using both stages through their combined <sample mean>.
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