1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Monte Carlo, logit illcond 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_illcond_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}{$m = 256$, $K = 4,096$} & \multicolumn{3}{c}{$m = 512$, $K = 2,048$} \\8 & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov & gap & RMSE & cov \\9\midrule10(1,0) plain average & 210.693 & 214.302 & 0.043 & 91.092 & 95.886 & 0.196 & 43.123 & 52.667 & 0.361 & 21.195 & 36.302 & 0.580 \\11(1,1) average + 1 Newton & 11.713 & 30.908 & 0.784 & 2.072 & 28.150 & 0.949 & 0.452 & 28.734 & 0.952 & 0.107 & 28.489 & 0.959 \\12(1,2) average + 2 Newton & 0.033 & 29.265 & 0.947 & 0.001 & 28.119 & 0.948 & 4.90e-5 & 28.745 & 0.951 & 2.71e-6 & 28.494 & 0.959 \\13(2,0) half-block jackknife & 2.71e+4 & 2.70e+4 & 0.005 & 47.520 & 54.771 & 0.466 & 10.088 & 30.604 & 0.900 & 5.965 & 29.151 & 0.953 \\14(2,1) half-block + 1 Newton & 6.94e+7 & 6.94e+7 & 0.004 & 1.181 & 28.130 & 0.949 & 0.011 & 28.745 & 0.951 & 0.002 & 28.494 & 0.959 \\15(2,2) half-block + 2 Newton & 3.79e+18 & 3.79e+18 & -- & 0.003 & 28.119 & -- & 2.34e-8 & 28.745 & -- & 4.98e-10 & 28.494 & -- \\16(3,0) quarter-block & 2.34e+5 & 2.34e+5 & -- & 5229.112 & 5228.017 & -- & 13.224 & 32.137 & -- & 8.334 & 29.798 & -- \\17(3,1) quarter-block + 1 Newton & 3.59e+10 & 3.59e+10 & 0.015 & 8.31e+4 & 8.31e+4 & 0.009 & 0.010 & 28.745 & 0.951 & 0.002 & 28.494 & 0.959 \\18analytic Cox--Snell + 1 Newton & 0.025 & 29.266 & 0.947 & 0.002 & 28.119 & 0.948 & 8.32e-4 & 28.745 & 0.951 & 3.88e-4 & 28.494 & 0.959 \\19CSL, 1 round & 245.222 & 246.526 & -- & 67.596 & 73.424 & -- & 21.791 & 35.857 & -- & 7.123 & 29.140 & -- \\20CSL, 2 rounds & 234.725 & 237.589 & -- & 29.868 & 40.629 & -- & 5.641 & 29.359 & -- & 1.101 & 28.482 & -- \\21AEE (Lin--Xi) & 154.527 & 155.672 & -- & 78.136 & 82.454 & -- & 39.644 & 48.319 & -- & 20.046 & 33.989 & -- \\22(2,1) stale Hessian & 2.50e+4 & 2.50e+4 & -- & 4.833 & 28.611 & -- & 0.383 & 28.741 & -- & 0.114 & 28.493 & -- \\23centralized MLE & 0 & 29.267 & 0.947 & 0 & 28.119 & 0.948 & 0 & 28.745 & 0.951 & 0 & 28.494 & 0.959 \\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): $m=64$: 0.973 / 0.022; $m=128$: 1.000 / 0.947; $m=256$: 1.000 / 1.000; $m=512$: 1.000 / 1.000.29\end{tablenotes}30\end{threeparttable}31\end{table}32