\begin{table}[p]
\centering\scriptsize
\begin{threeparttable}
\caption{Monte Carlo, logit misspec design, $p = 3$, $N = 262,144$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_misspec_p3}
\begin{tabular}{@{}lrrrrrr@{}}
\toprule
Estimator & \multicolumn{3}{c}{$m = 128$, $K = 2,048$} & \multicolumn{3}{c}{$m = 256$, $K = 1,024$} \\
 & gap & RMSE & cov & gap & RMSE & cov \\
\midrule
(1,0) plain average & 12.365 & 73.446 & 0.129 & 6.032 & 77.571 & 0.003 \\
(1,1) average + 1 Newton & 0.099 & 81.930 & 0.000 & 0.023 & 81.810 & 0.000 \\
(1,2) average + 2 Newton & 6.54e-6 & 81.854 & 0.000 & 3.65e-7 & 81.792 & 0.000 \\
(2,0) half-block jackknife & 1.668 & 82.831 & 0.000 & 0.714 & 82.009 & 0.000 \\
(2,1) half-block + 1 Newton & 0.002 & 81.856 & 0.000 & 3.61e-4 & 81.792 & 0.000 \\
(2,2) half-block + 2 Newton & 4.97e-9 & 81.854 & -- & 2.09e-10 & 81.792 & -- \\
(3,0) quarter-block & 13.789 & 81.339 & -- & 0.947 & 81.752 & -- \\
(3,1) quarter-block + 1 Newton & 2.251 & 81.978 & 0.000 & 6.00e-4 & 81.792 & 0.000 \\
analytic Cox--Snell + 1 Newton & 0.003 & 81.856 & 0.000 & 7.22e-4 & 81.792 & 0.000 \\
CSL, 1 round & 1.986 & 82.096 & -- & 0.666 & 81.850 & -- \\
CSL, 2 rounds & 0.564 & 81.610 & -- & 0.128 & 81.737 & -- \\
AEE (Lin--Xi) & 10.684 & 90.447 & -- & 5.413 & 86.086 & -- \\
(2,1) stale Hessian & 0.051 & 81.826 & -- & 0.011 & 81.789 & -- \\
centralized MLE & 0 & 81.854 & 0.000 & 0 & 81.792 & 0.000 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\footnotesize
\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 $\approx 0.007$.
\item Fraction of workers with all local fits valid (orders 2 / 3): $m=256$: 1.000 / 1.000; $m=128$: 1.000 / 1.000.
\end{tablenotes}
\end{threeparttable}
\end{table}