1\begin{table}[p]2\centering\scriptsize\setlength{\tabcolsep}{2.6pt}3\begin{threeparttable}4\caption{Monte Carlo, logit design, $p = 8$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$ (root mean square and median) 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 & median & cov & gap & median & cov & gap & median & cov & gap & median & cov \\9\midrule10(1,0) plain average & 233.988 & 226.445 & 0.000 & 94.917 & 94.867 & 0.000 & 21.491 & 21.476 & 0.148 & 10.589 & 10.579 & 0.633 \\11(1,1) average + 1 Newton & 31.375 & 23.351 & 0.099 & 3.908 & 3.903 & 0.910 & 0.195 & 0.194 & 0.952 & 0.047 & 0.047 & 0.953 \\12(1,2) average + 2 Newton & 2.099 & 0.225 & 0.939 & 0.006 & 0.006 & 0.956 & 1.59e-5 & 1.57e-5 & 0.952 & 9.30e-7 & 9.19e-7 & 0.953 \\13(2,0) half-block jackknife & 1.21e+5 & 1.83e+4 & 0.000 & 40.951 & 36.630 & 0.004 & 1.888 & 1.804 & 0.943 & 0.958 & 0.909 & 0.950 \\14(2,1) half-block + 1 Newton & 2.29e+11 & 2.30e+6 & 0.012 & 1.299 & 0.551 & 0.951 & 0.001 & 0.001 & 0.951 & 3.22e-4 & 2.26e-4 & 0.953 \\15(2,2) half-block + 2 Newton & 2.98e+24 & 1.66e+12 & -- & 0.007 & 1.27e-4 & -- & 1.40e-9 & 5.28e-10 & -- & 7.37e-11 & 2.05e-11 & -- \\16(3,0) quarter-block & 2.42e+5 & 8366.716 & -- & 3.85e+4 & 5907.183 & -- & 1.925 & 1.838 & -- & 1.281 & 1.218 & -- \\17(3,1) quarter-block + 1 Newton & 1.87e+12 & 1.81e+5 & 0.022 & 3.10e+9 & 4.36e+4 & 0.000 & 0.001 & 9.01e-4 & 0.952 & 5.11e-4 & 3.91e-4 & 0.953 \\18(2,1) valid workers only & 36.546 & 36.534 & -- & 0.550 & 0.548 & -- & -- & -- & -- & -- & -- & -- \\19(3,1) valid workers only & 18.571 & 16.983 & -- & 0.638 & 0.627 & -- & -- & -- & -- & -- & -- & -- \\20analytic Cox--Snell + 1 Newton & 1.84e+28 & 0.059 & 0.914 & 0.003 & 0.002 & 0.956 & 2.62e-4 & 1.90e-4 & 0.951 & 1.30e-4 & 9.20e-5 & 0.953 \\21CSL, 1 round & 74.154 & 66.001 & -- & 20.854 & 19.065 & -- & 2.097 & 1.973 & -- & 0.718 & 0.681 & -- \\22CSL, 2 rounds & 75.048 & 47.543 & -- & 11.224 & 8.233 & -- & 0.431 & 0.344 & -- & 0.101 & 0.083 & -- \\23AEE (Lin--Xi) & 163.653 & 163.589 & -- & 81.827 & 81.833 & -- & 20.707 & 20.711 & -- & 10.393 & 10.385 & -- \\24(2,1) stale Hessian & 1.20e+5 & 1.33e+4 & -- & 3.739 & 2.742 & -- & 0.031 & 0.030 & -- & 0.008 & 0.008 & -- \\25centralized MLE & 0 & -- & 0.943 & 0 & -- & 0.956 & 0 & -- & 0.952 & 0 & -- & 0.953 \\26\bottomrule27\end{tabular}28\begin{tablenotes}\footnotesize29\item 500/500/1000/1000/1000 paired replications per column. gap $=$ root mean square of $\sqrt N\,\lVert\tilde\theta - \widehat\theta_N\rVert$ over all replications (including those with failed local fits); median $=$ its median; 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 $\approx 0.010$ or less.30\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. Rows `valid workers only' drop the workers with a failed sub-block fit from the pilot (weights renormalized) and coincide with the corresponding rows when no fit failed.31\end{tablenotes}32\end{threeparttable}33\end{table}34