1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Monte Carlo, logit p20 design, $p = 20$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_p20_p20}5\begin{tabular}{@{}lrrrrrrrrrrrr@{}}6\toprule7Estimator & \multicolumn{3}{c}{$m = 128$, $K = 8,192$} & \multicolumn{3}{c}{$m = 256$, $K = 4,096$} & \multicolumn{3}{c}{$m = 1024$, $K = 1,024$} & \multicolumn{3}{c}{$m = 2048$, $K = 512$} \\8 & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov \\9\midrule10(1,0) plain average & 323.376 & 323.718 & 0.000 & 131.255 & 131.770 & 0.000 & 29.210 & 30.964 & 0.343 & 14.338 & 17.881 & 0.719 \\11(1,1) average + 1 Newton & 49.477 & 50.361 & 0.075 & 7.699 & 12.790 & 0.889 & 0.369 & 10.159 & 0.953 & 0.088 & 10.329 & 0.954 \\12(1,2) average + 2 Newton & 1.031 & 10.362 & 0.947 & 0.025 & 10.300 & 0.952 & 5.84e-5 & 10.155 & 0.953 & 3.37e-6 & 10.331 & 0.954 \\13(2,0) half-block jackknife & 1.65e+5 & 1.65e+5 & 0.000 & 61.069 & 61.824 & 0.033 & 3.171 & 10.608 & 0.941 & 1.668 & 10.468 & 0.947 \\14(2,1) half-block + 1 Newton & 2.26e+11 & 2.26e+11 & 0.066 & 1.564 & 10.400 & 0.947 & 0.004 & 10.155 & 0.953 & 9.12e-4 & 10.331 & 0.954 \\15(2,2) half-block + 2 Newton & 1.29e+131 & 1.29e+131 & -- & 0.001 & 10.301 & -- & 7.91e-9 & 10.155 & -- & 5.12e-10 & 10.331 & -- \\16(3,0) quarter-block & 3.25e+5 & 3.25e+5 & -- & 4.40e+4 & 4.40e+4 & -- & 3.404 & 10.700 & -- & 2.272 & 10.592 & -- \\17(3,1) quarter-block + 1 Newton & 1.84e+12 & 1.84e+12 & 0.899 & 4.14e+9 & 4.14e+9 & 0.008 & 0.003 & 10.155 & 0.953 & 0.002 & 10.331 & 0.954 \\18analytic Cox--Snell + 1 Newton & 0.253 & 10.331 & 0.949 & 0.009 & 10.300 & 0.952 & 7.34e-4 & 10.155 & 0.953 & 3.59e-4 & 10.331 & 0.954 \\19CSL, 1 round & 112.258 & 112.746 & -- & 29.269 & 31.021 & -- & 2.937 & 10.575 & -- & 1.017 & 10.358 & -- \\20CSL, 2 rounds & 141.077 & 141.505 & -- & 18.314 & 21.012 & -- & 0.691 & 10.182 & -- & 0.163 & 10.334 & -- \\21AEE (Lin--Xi) & 230.409 & 230.466 & -- & 112.533 & 112.893 & -- & 28.049 & 29.782 & -- & 14.027 & 17.221 & -- \\22(2,1) stale Hessian & 1.63e+5 & 1.63e+5 & -- & 6.341 & 12.156 & -- & 0.066 & 10.156 & -- & 0.018 & 10.331 & -- \\23centralized MLE & 0 & 10.332 & 0.948 & 0 & 10.301 & 0.952 & 0 & 10.155 & 0.953 & 0 & 10.331 & 0.954 \\24\bottomrule25\end{tabular}26\begin{tablenotes}\footnotesize27\item 500 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 $\approx 0.010$.28\item Fraction of workers with all local fits valid (orders 2 / 3): $m=128$: 0.821 / 0.000; $m=256$: 1.000 / 0.674; $m=512$: 1.000 / 1.000; $m=1024$: 1.000 / 1.000; $m=2048$: 1.000 / 1.000.29\end{tablenotes}30\end{threeparttable}31\end{table}32