1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Monte Carlo, logit design, $p = 3$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_p3}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 & 61.612 & 61.746 & 0.000 & 29.019 & 29.330 & 0.008 & 6.969 & 7.892 & 0.572 & 3.463 & 5.064 & 0.860 \\11(1,1) average + 1 Newton & 1.463 & 4.092 & 0.933 & 0.318 & 3.757 & 0.951 & 0.018 & 3.744 & 0.951 & 0.004 & 3.751 & 0.957 \\12(1,2) average + 2 Newton & 7.95e-4 & 3.831 & 0.949 & 3.76e-5 & 3.751 & 0.952 & 1.21e-7 & 3.744 & 0.951 & 6.47e-9 & 3.751 & 0.957 \\13(2,0) half-block jackknife & 3147.554 & 3147.627 & 0.020 & 3.782 & 5.308 & 0.829 & 0.514 & 3.775 & 0.949 & 0.338 & 3.769 & 0.958 \\14(2,1) half-block + 1 Newton & 1.19e+7 & 1.19e+7 & 0.898 & 0.006 & 3.751 & 0.952 & 1.09e-4 & 3.744 & 0.951 & 4.55e-5 & 3.751 & 0.957 \\15(2,2) half-block + 2 Newton & 3.52e+17 & 3.52e+17 & -- & 1.39e-8 & 3.751 & -- & 1.08e-9 & 3.744 & -- & 1.08e-9 & 3.751 & -- \\16(3,0) quarter-block & 7309.080 & 7309.149 & -- & 79.768 & 79.856 & -- & 0.678 & 3.792 & -- & 0.473 & 3.781 & -- \\17(3,1) quarter-block + 1 Newton & 9.24e+7 & 9.24e+7 & 0.001 & 144.811 & 144.911 & 0.947 & 1.73e-4 & 3.744 & 0.951 & 8.65e-5 & 3.751 & 0.957 \\18analytic Cox--Snell + 1 Newton & 5.38e-4 & 3.831 & 0.949 & 1.76e-4 & 3.751 & 0.952 & 4.49e-5 & 3.744 & 0.951 & 2.13e-5 & 3.751 & 0.957 \\19CSL, 1 round & 13.350 & 13.891 & -- & 4.334 & 5.683 & -- & 0.510 & 3.790 & -- & 0.170 & 3.754 & -- \\20CSL, 2 rounds & 6.175 & 7.230 & -- & 1.233 & 3.960 & -- & 0.064 & 3.744 & -- & 0.014 & 3.751 & -- \\21AEE (Lin--Xi) & 52.632 & 52.757 & -- & 26.847 & 27.041 & -- & 6.829 & 7.809 & -- & 3.423 & 5.119 & -- \\22(2,1) stale Hessian & 3046.272 & 3046.346 & -- & 0.102 & 3.753 & -- & 0.004 & 3.744 & -- & 0.001 & 3.751 & -- \\23centralized MLE & 0 & 3.831 & 0.949 & 0 & 3.751 & 0.952 & 0 & 3.744 & 0.951 & 0 & 3.751 & 0.957 \\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): $m=64$: 1.000 / 0.924; $m=128$: 1.000 / 1.000; $m=256$: 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