= Random-count central limit theorem for accepted rejection samples
{title2=$\sqrt n(\widehat\theta_{\rm rej}-\theta)\Rightarrow N(0,M\operatorname{Var}_f\phi)$}
Conditional iid accepted values have the ordinary target-sample CLT at scale $\sqrt N$. Since $N/n\to1/M$, the same estimator has asymptotic variance $M\operatorname{Var}_f\phi$ at scale $\sqrt n$. The centered count has limiting variance $(1/M)(1-1/M)$. Any fixed convention on an empty output is asymptotically negligible.
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