1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Monte Carlo, logit design, $p = 8$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_p8}5\begin{tabular}{@{}lrrrrrrrrrrrr@{}}6\toprule7Estimator & \multicolumn{3}{c}{$m = 64$, $K = 16,384$} & \multicolumn{3}{c}{$m = 128$, $K = 8,192$} & \multicolumn{3}{c}{$m = 512$, $K = 2,048$} & \multicolumn{3}{c}{$m = 1024$, $K = 1,024$} \\8 & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov \\9\midrule10(1,0) plain average & 233.195 & 233.424 & 0.000 & 94.927 & 95.224 & 0.000 & 21.491 & 22.386 & 0.148 & 10.589 & 12.356 & 0.633 \\11(1,1) average + 1 Newton & 31.483 & 32.009 & 0.099 & 3.909 & 7.327 & 0.916 & 0.195 & 6.304 & 0.952 & 0.047 & 6.342 & 0.953 \\12(1,2) average + 2 Newton & 2.275 & 6.848 & 0.942 & 0.006 & 6.260 & 0.956 & 1.59e-5 & 6.301 & 0.952 & 9.30e-7 & 6.342 & 0.953 \\13(2,0) half-block jackknife & 9.42e+4 & 9.42e+4 & 0.000 & 45.313 & 45.654 & 0.004 & 1.888 & 6.568 & 0.943 & 0.958 & 6.404 & 0.950 \\14(2,1) half-block + 1 Newton & 1.62e+11 & 1.62e+11 & 0.009 & 3.356 & 7.081 & 0.952 & 0.001 & 6.301 & 0.951 & 3.22e-4 & 6.342 & 0.953 \\15(2,2) half-block + 2 Newton & 2.38e+24 & 2.38e+24 & -- & 0.125 & 6.261 & -- & 1.40e-9 & 6.301 & -- & 7.37e-11 & 6.342 & -- \\16(3,0) quarter-block & 1.86e+5 & 1.86e+5 & -- & 2.85e+4 & 2.85e+4 & -- & 1.925 & 6.571 & -- & 1.281 & 6.458 & -- \\17(3,1) quarter-block + 1 Newton & 1.32e+12 & 1.32e+12 & 0.018 & 2.36e+9 & 2.36e+9 & 0.002 & 0.001 & 6.301 & 0.952 & 5.11e-4 & 6.342 & 0.953 \\18analytic Cox--Snell + 1 Newton & 9.07e+53 & 9.07e+53 & 0.918 & 0.003 & 6.260 & 0.956 & 2.62e-4 & 6.301 & 0.951 & 1.30e-4 & 6.342 & 0.953 \\19CSL, 1 round & 76.119 & 76.343 & -- & 20.125 & 21.127 & -- & 2.097 & 6.631 & -- & 0.718 & 6.378 & -- \\20CSL, 2 rounds & 80.931 & 81.210 & -- & 10.636 & 12.318 & -- & 0.431 & 6.314 & -- & 0.101 & 6.344 & -- \\21AEE (Lin--Xi) & 163.596 & 163.586 & -- & 81.848 & 81.995 & -- & 20.707 & 21.655 & -- & 10.393 & 12.159 & -- \\22(2,1) stale Hessian & 9.31e+4 & 9.31e+4 & -- & 7.823 & 10.074 & -- & 0.031 & 6.301 & -- & 0.008 & 6.342 & -- \\23centralized MLE & 0 & 6.495 & 0.945 & 0 & 6.260 & 0.956 & 0 & 6.301 & 0.952 & 0 & 6.342 & 0.953 \\24\bottomrule25\end{tabular}26\begin{tablenotes}\footnotesize27\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 $\approx 0.007$.28\item Fraction of workers with all local fits valid (orders 2 / 3): $m=64$: 0.930 / 0.009; $m=128$: 1.000 / 0.865; $m=256$: 1.000 / 1.000; $m=512$: 1.000 / 1.000; $m=1024$: 1.000 / 1.000.29\end{tablenotes}30\end{threeparttable}31\end{table}32