1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Monte Carlo, exp design, $p = 1$, $N = 262,144$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_exp_p1}5\begin{tabular}{@{}lrrrrrrrrrrrrrrrrrrrrrrrr@{}}6\toprule7Estimator & \multicolumn{3}{c}{$m = 8$, $K = 32,768$} & \multicolumn{3}{c}{$m = 16$, $K = 16,384$} & \multicolumn{3}{c}{$m = 32$, $K = 8,192$} & \multicolumn{3}{c}{$m = 64$, $K = 4,096$} & \multicolumn{3}{c}{$m = 128$, $K = 2,048$} & \multicolumn{3}{c}{$m = 256$, $K = 1,024$} & \multicolumn{3}{c}{$m = 512$, $K = 512$} & \multicolumn{3}{c}{$m = 1024$, $K = 256$} \\8 & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov \\9\midrule10(1,0) plain average & 73.146 & 73.177 & 0.000 & 34.124 & 34.152 & 0.000 & 16.520 & 16.548 & 0.000 & 8.125 & 8.231 & 0.000 & 4.034 & 4.191 & 0.016 & 2.005 & 2.220 & 0.493 & 1.005 & 1.413 & 0.829 & 0.500 & 1.098 & 0.921 \\11(1,1) average + 1 Newton & 10.451 & 10.474 & 0.000 & 2.275 & 2.476 & 0.371 & 0.533 & 1.143 & 0.906 & 0.129 & 1.002 & 0.950 & 0.032 & 0.978 & 0.958 & 0.008 & 0.995 & 0.954 & 0.002 & 0.996 & 0.949 & 4.96e-4 & 0.994 & 0.951 \\12(1,2) average + 2 Newton & 0.213 & 1.008 & 0.952 & 0.010 & 1.007 & 0.948 & 5.57e-4 & 1.009 & 0.952 & 3.27e-5 & 0.999 & 0.947 & 2.00e-6 & 0.979 & 0.958 & 1.23e-7 & 0.994 & 0.956 & 7.96e-9 & 0.996 & 0.949 & 5.11e-10 & 0.994 & 0.950 \\13(2,0) half-block jackknife & 24.405 & 24.402 & 0.000 & 4.921 & 5.013 & 0.006 & 1.159 & 1.540 & 0.777 & 0.380 & 1.055 & 0.934 & 0.195 & 0.997 & 0.949 & 0.129 & 1.006 & 0.954 & 0.090 & 0.996 & 0.947 & 0.063 & 0.998 & 0.949 \\14(2,1) half-block + 1 Newton & 1.169 & 1.514 & 0.791 & 0.049 & 1.008 & 0.946 & 0.003 & 1.009 & 0.953 & 4.50e-4 & 0.999 & 0.947 & 1.25e-4 & 0.979 & 0.958 & 5.65e-5 & 0.994 & 0.956 & 2.85e-5 & 0.996 & 0.949 & 1.34e-5 & 0.994 & 0.950 \\15(2,2) half-block + 2 Newton & 0.003 & 0.990 & -- & 5.25e-6 & 1.007 & -- & 3.19e-8 & 1.009 & -- & 1.12e-9 & 0.999 & -- & 1.09e-10 & 0.979 & -- & 2.30e-11 & 0.994 & -- & 7.79e-12 & 0.996 & -- & 1.14e-12 & 0.994 & -- \\16(3,0) quarter-block & 24.625 & 24.669 & -- & 1.893 & 2.159 & -- & 0.590 & 1.169 & -- & 0.387 & 1.067 & -- & 0.265 & 1.018 & -- & 0.179 & 1.013 & -- & 0.127 & 0.998 & -- & 0.088 & 1.000 & -- \\17(3,1) quarter-block + 1 Newton & 1.281 & 1.602 & 0.788 & 0.010 & 1.007 & 0.948 & 0.001 & 1.009 & 0.953 & 5.03e-4 & 0.999 & 0.947 & 2.37e-4 & 0.979 & 0.958 & 1.09e-4 & 0.994 & 0.956 & 5.74e-5 & 0.996 & 0.949 & 2.62e-5 & 0.994 & 0.950 \\18analytic Cox--Snell + 1 Newton & 0.001 & 0.990 & 0.954 & 4.87e-4 & 1.007 & 0.948 & 2.25e-4 & 1.009 & 0.952 & 1.12e-4 & 0.999 & 0.947 & 5.57e-5 & 0.979 & 0.958 & 2.81e-5 & 0.994 & 0.956 & 1.39e-5 & 0.996 & 0.949 & 6.64e-6 & 0.994 & 0.950 \\19CSL, 1 round & 7.57e-14 & 0.990 & -- & 7.61e-14 & 1.007 & -- & 7.25e-14 & 1.009 & -- & 7.88e-14 & 0.999 & -- & 7.24e-14 & 0.979 & -- & 7.73e-14 & 0.994 & -- & 7.51e-14 & 0.996 & -- & 7.73e-14 & 0.994 & -- \\20CSL, 2 rounds & 7.88e-14 & 0.990 & -- & 7.20e-14 & 1.007 & -- & 7.59e-14 & 1.009 & -- & 7.71e-14 & 0.999 & -- & 7.24e-14 & 0.979 & -- & 7.58e-14 & 0.994 & -- & 7.63e-14 & 0.996 & -- & 8.10e-14 & 0.994 & -- \\21AEE (Lin--Xi) & 56.889 & 56.874 & -- & 30.110 & 30.114 & -- & 15.518 & 15.553 & -- & 7.875 & 7.892 & -- & 3.972 & 4.051 & -- & 1.990 & 2.242 & -- & 1.001 & 1.413 & -- & 0.499 & 1.127 & -- \\22(2,1) stale Hessian & 1.622 & 1.880 & -- & 0.243 & 1.033 & -- & 0.032 & 1.010 & -- & 0.005 & 0.999 & -- & 0.001 & 0.979 & -- & 4.86e-4 & 0.995 & -- & 1.74e-4 & 0.996 & -- & 6.30e-5 & 0.994 & -- \\23centralized MLE & 0 & 0.990 & 0.954 & 0 & 1.007 & 0.948 & 0 & 1.009 & 0.953 & 0 & 0.999 & 0.947 & 0 & 0.979 & 0.958 & 0 & 0.994 & 0.956 & 0 & 0.996 & 0.949 & 0 & 0.994 & 0.950 \\24\bottomrule25\end{tabular}26\begin{tablenotes}\footnotesize27\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 $\approx 0.005$.28\item Fraction of workers with all local fits valid (orders 2 / 3): $m=256$: 1.000 / 1.000; $m=16$: 1.000 / 1.000; $m=128$: 1.000 / 1.000; $m=1024$: 1.000 / 1.000; $m=8$: 1.000 / 1.000; $m=64$: 1.000 / 1.000; $m=512$: 1.000 / 1.000; $m=32$: 1.000 / 1.000.29\end{tablenotes}30\end{threeparttable}31\end{table}32