1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Monte Carlo, pois design, $p = 3$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$ (root mean square and median) and 95\% coverage by local sample size $m$.}\label{tab:mc_pois_p3}5\begin{tabular}{@{}lrrrrrrrrrrrr@{}}6\toprule7Estimator & \multicolumn{3}{c}{$m = 32$, $K = 32,768$} & \multicolumn{3}{c}{$m = 128$, $K = 8,192$} & \multicolumn{3}{c}{$m = 512$, $K = 2,048$} & \multicolumn{3}{c}{$m = 1024$, $K = 1,024$} \\8 & gap & median & cov & gap & median & cov & gap & median & cov & gap & median & cov \\9\midrule10(1,0) plain average & 41.906 & 41.910 & 0.145 & 9.934 & 9.932 & 0.630 & 2.461 & 2.460 & 0.727 & 1.229 & 1.225 & 0.877 \\11(1,1) average + 1 Newton & 0.882 & 0.882 & 0.905 & 0.049 & 0.048 & 0.949 & 0.003 & 0.003 & 0.951 & 7.49e-4 & 7.43e-4 & 0.947 \\12(1,2) average + 2 Newton & 3.97e-4 & 3.97e-4 & 0.944 & 1.16e-6 & 1.16e-6 & 0.949 & 3.88e-9 & 3.81e-9 & 0.951 & 3.52e-10 & 3.51e-10 & 0.946 \\13(2,0) half-block jackknife & 12.288 & 9.597 & 0.007 & 0.721 & 0.678 & 0.926 & 0.221 & 0.193 & 0.948 & 0.154 & 0.136 & 0.947 \\14(2,1) half-block + 1 Newton & 0.768 & 0.053 & 0.941 & 3.25e-4 & 2.39e-4 & 0.949 & 3.89e-5 & 2.16e-5 & 0.951 & 1.84e-5 & 1.05e-5 & 0.946 \\15(2,2) half-block + 2 Newton & 0.009 & 1.65e-6 & -- & 5.70e-10 & 5.77e-10 & -- & 6.11e-10 & 6.09e-10 & -- & 6.12e-10 & 6.12e-10 & -- \\16(3,0) quarter-block & 1210.274 & 223.376 & -- & 0.650 & 0.569 & -- & 0.309 & 0.269 & -- & 0.218 & 0.191 & -- \\17(3,1) quarter-block + 1 Newton & 1192.998 & 30.713 & 0.014 & 3.30e-4 & 1.89e-4 & 0.949 & 7.58e-5 & 4.16e-5 & 0.951 & 3.72e-5 & 2.09e-5 & 0.946 \\18(2,1) valid workers only & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- \\19(3,1) valid workers only & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- \\20analytic Cox--Snell + 1 Newton & 3.65e-4 & 2.25e-4 & 0.944 & 7.83e-5 & 4.51e-5 & 0.949 & 1.81e-5 & 1.04e-5 & 0.951 & 8.83e-6 & 5.59e-6 & 0.946 \\21CSL, 1 round & 14.351 & 9.883 & -- & 1.368 & 1.057 & -- & 0.172 & 0.139 & -- & 0.060 & 0.050 & -- \\22CSL, 2 rounds & 22.792 & 4.201 & -- & 0.500 & 0.199 & -- & 0.026 & 0.014 & -- & 0.006 & 0.003 & -- \\23AEE (Lin--Xi) & 40.398 & 40.398 & -- & 9.860 & 9.859 & -- & 2.450 & 2.449 & -- & 1.223 & 1.223 & -- \\24(2,1) stale Hessian & 0.803 & 0.083 & -- & 0.004 & 0.003 & -- & 3.24e-4 & 2.46e-4 & -- & 1.16e-4 & 9.14e-5 & -- \\25centralized MLE & 0 & -- & 0.944 & 0 & -- & 0.949 & 0 & -- & 0.951 & 0 & -- & 0.946 \\26\bottomrule27\end{tabular}28\begin{tablenotes}\footnotesize29\item 1000 paired replications per column. gap $=$ root mean square of $\sqrt N\,\lVert\tilde\theta - \widehat\theta_N\rVert$ over all replications (including those with failed local fits); median $=$ its median; cov $=$ empirical coverage of nominal 95\% Wald intervals (observed information at the estimate; `--' when not computed). Monte Carlo standard errors of the gaps and RMSEs are in \texttt{results/processed/summary.csv}; coverage standard error $\approx 0.007$ or less.30\item Fraction of workers with all local fits valid (orders 2 / 3): $m=32$: 1.000 / 1.000; $m=64$: 1.000 / 1.000; $m=128$: 1.000 / 1.000; $m=256$: 1.000 / 1.000; $m=512$: 1.000 / 1.000; $m=1024$: 1.000 / 1.000. Rows `valid workers only' drop the workers with a failed sub-block fit from the pilot (weights renormalized) and coincide with the corresponding rows when no fit failed.31\end{tablenotes}32\end{threeparttable}33\end{table}34