1\begin{table}[p]2\centering\scriptsize\setlength{\tabcolsep}{2.6pt}3\begin{threeparttable}4\caption{Monte Carlo, logit design, $p = 3$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$ (root mean square and median) and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_p3}5\begin{tabular}{@{}lrrrrrrrrrrrr@{}}6\toprule7Estimator & \multicolumn{3}{c}{$m = 32$, $K = 32,768$} & \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 & 286.566 & 149.017 & 0.000 & 29.019 & 29.016 & 0.008 & 6.969 & 6.973 & 0.572 & 3.463 & 3.457 & 0.860 \\11(1,1) average + 1 Newton & 2689.961 & 9.014 & 0.331 & 0.318 & 0.318 & 0.951 & 0.018 & 0.018 & 0.951 & 0.004 & 0.004 & 0.957 \\12(1,2) average + 2 Newton & 8.41e+6 & 0.030 & 0.945 & 3.76e-5 & 3.75e-5 & 0.952 & 1.21e-7 & 1.20e-7 & 0.951 & 6.47e-9 & 6.22e-9 & 0.957 \\13(2,0) half-block jackknife & 1.45e+4 & 8938.189 & 0.000 & 3.782 & 3.678 & 0.829 & 0.514 & 0.434 & 0.949 & 0.338 & 0.296 & 0.958 \\14(2,1) half-block + 1 Newton & 2.04e+8 & 2.36e+5 & 0.004 & 0.006 & 0.005 & 0.952 & 1.09e-4 & 4.71e-5 & 0.951 & 4.55e-5 & 2.19e-5 & 0.957 \\15(2,2) half-block + 2 Newton & 1.18e+24 & 2.30e+9 & -- & 1.39e-8 & 7.90e-9 & -- & 1.08e-9 & 1.07e-9 & -- & 1.08e-9 & 1.08e-9 & -- \\16(3,0) quarter-block & 2.50e+4 & 2910.682 & -- & 79.768 & 4.556 & -- & 0.678 & 0.594 & -- & 0.473 & 0.422 & -- \\17(3,1) quarter-block + 1 Newton & 1.52e+9 & 7587.587 & 0.008 & 144.811 & 0.007 & 0.947 & 1.73e-4 & 8.65e-5 & 0.951 & 8.65e-5 & 4.37e-5 & 0.957 \\18(2,1) valid workers only & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- \\19(3,1) valid workers only & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- & -- \\20analytic Cox--Snell + 1 Newton & 4.62e+117 & 2.76e+12 & 0.457 & 1.76e-4 & 9.11e-5 & 0.952 & 4.49e-5 & 2.05e-5 & 0.951 & 2.13e-5 & 9.97e-6 & 0.957 \\21CSL, 1 round & 57.743 & 39.925 & -- & 4.334 & 3.654 & -- & 0.510 & 0.442 & -- & 0.170 & 0.150 & -- \\22CSL, 2 rounds & 50.483 & 15.308 & -- & 1.233 & 0.691 & -- & 0.064 & 0.040 & -- & 0.014 & 0.009 & -- \\23AEE (Lin--Xi) & 102.585 & 102.562 & -- & 26.847 & 26.836 & -- & 6.829 & 6.827 & -- & 3.423 & 3.422 & -- \\24(2,1) stale Hessian & 1.24e+4 & 5469.786 & -- & 0.102 & 0.099 & -- & 0.004 & 0.003 & -- & 0.001 & 0.001 & -- \\25centralized MLE & 0 & -- & 0.950 & 0 & -- & 0.952 & 0 & -- & 0.951 & 0 & -- & 0.957 \\26\bottomrule27\end{tabular}28\begin{tablenotes}\footnotesize29\item 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 $\approx 0.007$ or less.30\item Fraction of workers with all local fits valid (orders 2 / 3): $m=32$: 0.961 / 0.234; $m=64$: 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. 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