1\begin{table}[p]2\centering\scriptsize3\begin{threeparttable}4\caption{Monte Carlo, logit illcond design, $p = 8$, $N = 262,144$: 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}{@{}lrrr@{}}6\toprule7Estimator & \multicolumn{3}{c}{$m = 128$, $K = 2,048$} \\8 & gap & RMSE & cov \\9\midrule10(1,0) plain average & 46.067 & 55.084 & 0.358 \\11(1,1) average + 1 Newton & 1.044 & 28.518 & 0.949 \\12(1,2) average + 2 Newton & 5.21e-4 & 28.540 & 0.952 \\13(2,0) half-block jackknife & 80.014 & 84.567 & 0.681 \\14(2,1) half-block + 1 Newton & 3.465 & 28.771 & 0.951 \\15(2,2) half-block + 2 Newton & 0.035 & 28.540 & -- \\16(3,0) quarter-block & 7.08e+4 & 7.08e+4 & -- \\17(3,1) quarter-block + 1 Newton & 8.75e+9 & 8.75e+9 & 0.018 \\18analytic Cox--Snell + 1 Newton & 0.004 & 28.540 & 0.952 \\19CSL, 1 round & 32.901 & 43.974 & -- \\20CSL, 2 rounds & 14.917 & 32.553 & -- \\21AEE (Lin--Xi) & 39.134 & 47.574 & -- \\22(2,1) stale Hessian & 9.812 & 30.265 & -- \\23centralized MLE & 0 & 28.540 & 0.952 \\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): $m=128$: 1.000 / 0.946.29\end{tablenotes}30\end{threeparttable}31\end{table}32