1\begin{table}[p]2\centering\scriptsize\setlength{\tabcolsep}{2.6pt}3\begin{threeparttable}4\caption{Monte Carlo, pois design, $p = 8$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$ (root mean square and median) and 95\% coverage by local sample size $m$.}\label{tab:mc_pois_p8}5\begin{tabular}{@{}lrrrrrrrrrrrr@{}}6\toprule7Estimator & \multicolumn{3}{c}{$m = 64$, $K = 16,384$} & \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 & 53.236 & 53.245 & 0.354 & 25.472 & 25.475 & 0.777 & 6.187 & 6.184 & 0.829 & 3.082 & 3.078 & 0.845 \\11(1,1) average + 1 Newton & 1.433 & 1.433 & 0.917 & 0.322 & 0.322 & 0.948 & 0.019 & 0.019 & 0.951 & 0.005 & 0.005 & 0.949 \\12(1,2) average + 2 Newton & 0.001 & 0.001 & 0.952 & 5.19e-5 & 5.18e-5 & 0.948 & 1.80e-7 & 1.79e-7 & 0.951 & 1.15e-8 & 1.13e-8 & 0.949 \\13(2,0) half-block jackknife & 14.549 & 14.547 & 0.065 & 3.503 & 3.484 & 0.732 & 0.612 & 0.587 & 0.944 & 0.406 & 0.393 & 0.946 \\14(2,1) half-block + 1 Newton & 0.108 & 0.107 & 0.951 & 0.006 & 0.006 & 0.948 & 2.22e-4 & 1.86e-4 & 0.951 & 1.02e-4 & 8.48e-5 & 0.949 \\15(2,2) half-block + 2 Newton & 6.53e-6 & 6.32e-6 & -- & 2.13e-8 & 1.76e-8 & -- & 4.59e-11 & 2.07e-11 & -- & 9.93e-12 & 4.46e-12 & -- \\16(3,0) quarter-block & 618.373 & 304.800 & -- & 1.891 & 1.828 & -- & 0.805 & 0.770 & -- & 0.568 & 0.544 & -- \\17(3,1) quarter-block + 1 Newton & 534.838 & 54.517 & 0.055 & 0.002 & 0.002 & 0.948 & 4.04e-4 & 3.27e-4 & 0.951 & 2.01e-4 & 1.61e-4 & 0.949 \\18(2,1) valid workers only & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- \\19(3,1) valid workers only & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- \\20analytic Cox--Snell + 1 Newton & 9.78e-4 & 7.84e-4 & 0.952 & 4.10e-4 & 3.31e-4 & 0.948 & 9.93e-5 & 8.02e-5 & 0.951 & 4.91e-5 & 3.85e-5 & 0.949 \\21CSL, 1 round & 25.196 & 21.206 & -- & 7.563 & 6.728 & -- & 0.845 & 0.791 & -- & 0.294 & 0.279 & -- \\22CSL, 2 rounds & 39.205 & 18.291 & -- & 5.394 & 3.233 & -- & 0.219 & 0.156 & -- & 0.048 & 0.039 & -- \\23AEE (Lin--Xi) & 51.852 & 51.847 & -- & 25.195 & 25.185 & -- & 6.159 & 6.160 & -- & 3.063 & 3.062 & -- \\24(2,1) stale Hessian & 0.063 & 0.062 & -- & 0.011 & 0.010 & -- & 9.31e-4 & 8.25e-4 & -- & 3.32e-4 & 2.94e-4 & -- \\25centralized MLE & 0 & -- & 0.952 & 0 & -- & 0.948 & 0 & -- & 0.951 & 0 & -- & 0.949 \\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): $m=64$: 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