\begin{table}[p]
\centering\scriptsize
\begin{threeparttable}
\caption{Monte Carlo, pois design, $p = 3$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_pois_p3}
\begin{tabular}{@{}lrrrrrrrrrrrr@{}}
\toprule
Estimator & \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}{$m = 1024$, $K = 1,024$} \\
 & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov \\
\midrule
(1,0) plain average & 41.906 & 41.897 & 0.145 & 9.934 & 10.073 & 0.630 & 2.461 & 2.932 & 0.727 & 1.229 & 2.042 & 0.877 \\
(1,1) average + 1 Newton & 0.882 & 1.857 & 0.905 & 0.049 & 1.572 & 0.949 & 0.003 & 1.613 & 0.951 & 7.49e-4 & 1.611 & 0.947 \\
(1,2) average + 2 Newton & 3.97e-4 & 1.615 & 0.944 & 1.16e-6 & 1.572 & 0.949 & 3.88e-9 & 1.613 & 0.951 & 3.52e-10 & 1.611 & 0.946 \\
(2,0) half-block jackknife & 12.288 & 12.374 & 0.007 & 0.721 & 1.723 & 0.926 & 0.221 & 1.630 & 0.948 & 0.154 & 1.620 & 0.947 \\
(2,1) half-block + 1 Newton & 0.768 & 1.768 & 0.941 & 3.25e-4 & 1.572 & 0.949 & 3.89e-5 & 1.613 & 0.951 & 1.84e-5 & 1.611 & 0.946 \\
(2,2) half-block + 2 Newton & 0.009 & 1.615 & -- & 5.70e-10 & 1.572 & -- & 6.11e-10 & 1.613 & -- & 6.12e-10 & 1.611 & -- \\
(3,0) quarter-block & 1210.274 & 1210.265 & -- & 0.650 & 1.699 & -- & 0.309 & 1.642 & -- & 0.218 & 1.627 & -- \\
(3,1) quarter-block + 1 Newton & 1192.998 & 1192.993 & 0.014 & 3.30e-4 & 1.572 & 0.949 & 7.58e-5 & 1.613 & 0.951 & 3.72e-5 & 1.611 & 0.946 \\
analytic Cox--Snell + 1 Newton & 3.65e-4 & 1.615 & 0.944 & 7.83e-5 & 1.572 & 0.949 & 1.81e-5 & 1.613 & 0.951 & 8.83e-6 & 1.611 & 0.946 \\
CSL, 1 round & 14.351 & 14.484 & -- & 1.368 & 2.089 & -- & 0.172 & 1.624 & -- & 0.060 & 1.612 & -- \\
CSL, 2 rounds & 22.792 & 22.808 & -- & 0.500 & 1.647 & -- & 0.026 & 1.613 & -- & 0.006 & 1.611 & -- \\
AEE (Lin--Xi) & 40.398 & 40.470 & -- & 9.860 & 9.969 & -- & 2.450 & 2.945 & -- & 1.223 & 2.007 & -- \\
(2,1) stale Hessian & 0.803 & 1.826 & -- & 0.004 & 1.572 & -- & 3.24e-4 & 1.613 & -- & 1.16e-4 & 1.611 & -- \\
centralized MLE & 0 & 1.615 & 0.944 & 0 & 1.572 & 0.949 & 0 & 1.613 & 0.951 & 0 & 1.611 & 0.946 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\footnotesize
\item 1000 paired replications per column. gap $=$ root mean square of $\sqrt N\,\lVert\tilde\theta - \widehat\theta_N\rVert$; RMSE $=$ root mean square of $\sqrt N\,\lVert\tilde\theta - \theta_0\rVert$; 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 $\approx 0.007$.
\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.
\end{tablenotes}
\end{threeparttable}
\end{table}