= Conditional bias-corrected normal mean estimate
{title2=$m=d+(w/\sqrt{I_1})\phi(d\sqrt{I_1}-f)/\Phi(d\sqrt{I_1}-f)$}
In a two-stage normal trial, invert the pooled <estimator>'s conditional mean after continuation to correct its selection shift. The root is unique when the pooled stage-1 weight satisfies $0<w<1$, because its conditional-mean map has derivative between $1-w$ and one. This root also maximizes the corresponding conditional <likelihood>. It is distinct from exact conditional unbiasedness, which is supplied by a suitable <Rao-Blackwell theorem> construction.
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