\begin{table}[p]
\centering\scriptsize
\begin{threeparttable}
\caption{Monte Carlo, pois design, $p = 8$, $N = 262,144$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_pois_p8}
\begin{tabular}{@{}lrrrrrrrrr@{}}
\toprule
Estimator & \multicolumn{3}{c}{$m = 256$, $K = 1,024$} & \multicolumn{3}{c}{$m = 512$, $K = 512$} & \multicolumn{3}{c}{$m = 1024$, $K = 256$} \\
 & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov \\
\midrule
(1,0) plain average & 6.250 & 6.728 & 0.831 & 3.103 & 4.012 & 0.841 & 1.553 & 2.938 & 0.912 \\
(1,1) average + 1 Newton & 0.039 & 2.516 & 0.951 & 0.010 & 2.545 & 0.946 & 0.002 & 2.511 & 0.949 \\
(1,2) average + 2 Newton & 1.57e-6 & 2.516 & 0.951 & 1.02e-7 & 2.545 & 0.947 & 7.28e-9 & 2.511 & 0.949 \\
(2,0) half-block jackknife & 0.924 & 2.672 & 0.935 & 0.575 & 2.606 & 0.939 & 0.399 & 2.543 & 0.944 \\
(2,1) half-block + 1 Newton & 9.83e-4 & 2.516 & 0.951 & 4.08e-4 & 2.545 & 0.947 & 1.99e-4 & 2.511 & 0.949 \\
(2,2) half-block + 2 Newton & 1.68e-9 & 2.516 & -- & 3.48e-10 & 2.545 & -- & 8.56e-11 & 2.511 & -- \\
(3,0) quarter-block & 1.183 & 2.771 & -- & 0.806 & 2.664 & -- & 0.562 & 2.578 & -- \\
(3,1) quarter-block + 1 Newton & 0.002 & 2.516 & 0.951 & 8.08e-4 & 2.545 & 0.947 & 3.98e-4 & 2.511 & 0.949 \\
analytic Cox--Snell + 1 Newton & 3.91e-4 & 2.516 & 0.951 & 1.95e-4 & 2.545 & 0.947 & 9.82e-5 & 2.511 & 0.949 \\
CSL, 1 round & 1.249 & 2.791 & -- & 0.432 & 2.586 & -- & 0.152 & 2.519 & -- \\
CSL, 2 rounds & 0.494 & 2.563 & -- & 0.110 & 2.545 & -- & 0.026 & 2.511 & -- \\
AEE (Lin--Xi) & 6.200 & 6.700 & -- & 3.072 & 3.992 & -- & 1.529 & 2.952 & -- \\
(2,1) stale Hessian & 0.003 & 2.516 & -- & 0.001 & 2.545 & -- & 4.32e-4 & 2.511 & -- \\
centralized MLE & 0 & 2.516 & 0.951 & 0 & 2.545 & 0.947 & 0 & 2.511 & 0.949 \\
\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): $m=256$: 1.000 / 1.000; $m=1024$: 1.000 / 1.000; $m=512$: 1.000 / 1.000.
\end{tablenotes}
\end{threeparttable}
\end{table}