\begin{table}[p]
\centering\scriptsize
\begin{threeparttable}
\caption{Monte Carlo, exp design, $p = 1$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_exp_p1}
\begin{tabular}{@{}lrrrrrrrrrrrr@{}}
\toprule
Estimator & \multicolumn{3}{c}{$m = 8$, $K = 131,072$} & \multicolumn{3}{c}{$m = 32$, $K = 32,768$} & \multicolumn{3}{c}{$m = 256$, $K = 4,096$} & \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 & 146.302 & 146.312 & 0.000 & 33.039 & 33.022 & 0.000 & 4.020 & 4.122 & 0.021 & 1.002 & 1.433 & 0.827 \\
(1,1) average + 1 Newton & 20.903 & 20.921 & 0.000 & 1.066 & 1.483 & 0.802 & 0.016 & 0.975 & 0.955 & 9.84e-4 & 0.995 & 0.952 \\
(1,2) average + 2 Newton & 0.427 & 1.094 & 0.929 & 0.001 & 0.997 & 0.951 & 2.45e-7 & 0.974 & 0.956 & 9.60e-10 & 0.995 & 0.952 \\
(2,0) half-block jackknife & 48.771 & 48.775 & 0.000 & 2.239 & 2.480 & 0.410 & 0.128 & 0.984 & 0.952 & 0.063 & 0.997 & 0.952 \\
(2,1) half-block + 1 Newton & 2.326 & 2.529 & 0.364 & 0.005 & 0.997 & 0.951 & 2.76e-5 & 0.974 & 0.956 & 6.55e-6 & 0.995 & 0.952 \\
(2,2) half-block + 2 Newton & 0.005 & 1.010 & -- & 3.17e-8 & 0.997 & -- & 2.58e-12 & 0.974 & -- & 2.06e-13 & 0.995 & -- \\
(3,0) quarter-block & 48.902 & 48.918 & -- & 0.649 & 1.188 & -- & 0.177 & 0.992 & -- & 0.090 & 0.999 & -- \\
(3,1) quarter-block + 1 Newton & 2.359 & 2.562 & 0.360 & 7.11e-4 & 0.997 & 0.951 & 5.13e-5 & 0.974 & 0.956 & 1.34e-5 & 0.995 & 0.952 \\
analytic Cox--Snell + 1 Newton & 5.66e-4 & 1.010 & 0.951 & 1.14e-4 & 0.997 & 0.951 & 1.31e-5 & 0.974 & 0.956 & 3.13e-6 & 0.995 & 0.952 \\
CSL, 1 round & 1.49e-13 & 1.010 & -- & 1.48e-13 & 0.997 & -- & 1.50e-13 & 0.974 & -- & 1.44e-13 & 0.995 & -- \\
CSL, 2 rounds & 1.57e-13 & 1.010 & -- & 1.55e-13 & 0.997 & -- & 1.50e-13 & 0.974 & -- & 1.52e-13 & 0.995 & -- \\
AEE (Lin--Xi) & 113.780 & 113.779 & -- & 31.035 & 31.084 & -- & 3.988 & 4.120 & -- & 1.000 & 1.390 & -- \\
(2,1) stale Hessian & 3.249 & 3.397 & -- & 0.063 & 1.001 & -- & 4.85e-4 & 0.974 & -- & 6.21e-5 & 0.995 & -- \\
centralized MLE & 0 & 1.010 & 0.951 & 0 & 0.997 & 0.951 & 0 & 0.974 & 0.956 & 0 & 0.995 & 0.952 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\footnotesize
\item 2000 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 $\approx 0.005$.
\item Fraction of workers with all local fits valid (orders 2 / 3): $m=8$: 1.000 / 1.000; $m=16$: 1.000 / 1.000; $m=32$: 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}