\begin{table}[p]
\centering\scriptsize
\begin{threeparttable}
\caption{Monte Carlo, logit p20 design, $p = 20$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_p20_p20}
\begin{tabular}{@{}lrrrrrr@{}}
\toprule
Estimator & \multicolumn{3}{c}{$m = 1024$, $K = 1,024$} & \multicolumn{3}{c}{$m = 2048$, $K = 512$} \\
 & gap & RMSE & cov & gap & RMSE & cov \\
\midrule
(1,0) plain average & 29.210 & 30.964 & 0.343 & 14.338 & 17.881 & 0.719 \\
(1,1) average + 1 Newton & 0.369 & 10.159 & 0.953 & 0.088 & 10.329 & 0.954 \\
(1,2) average + 2 Newton & 5.84e-5 & 10.155 & 0.953 & 3.37e-6 & 10.331 & 0.954 \\
(2,0) half-block jackknife & 3.171 & 10.608 & 0.941 & 1.668 & 10.468 & 0.947 \\
(2,1) half-block + 1 Newton & 0.004 & 10.155 & 0.953 & 9.12e-4 & 10.331 & 0.954 \\
(2,2) half-block + 2 Newton & 7.91e-9 & 10.155 & -- & 5.12e-10 & 10.331 & -- \\
(3,0) quarter-block & 3.404 & 10.700 & -- & 2.272 & 10.592 & -- \\
(3,1) quarter-block + 1 Newton & 0.003 & 10.155 & 0.953 & 0.002 & 10.331 & 0.954 \\
analytic Cox--Snell + 1 Newton & 7.34e-4 & 10.155 & 0.953 & 3.59e-4 & 10.331 & 0.954 \\
CSL, 1 round & 2.937 & 10.575 & -- & 1.017 & 10.358 & -- \\
CSL, 2 rounds & 0.691 & 10.182 & -- & 0.163 & 10.334 & -- \\
AEE (Lin--Xi) & 28.049 & 29.782 & -- & 14.027 & 17.221 & -- \\
(2,1) stale Hessian & 0.066 & 10.156 & -- & 0.018 & 10.331 & -- \\
centralized MLE & 0 & 10.155 & 0.953 & 0 & 10.331 & 0.954 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\footnotesize
\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 $\approx 0.010$.
\item Fraction of workers with all local fits valid (orders 2 / 3): $m=1024$: 1.000 / 1.000; $m=2048$: 1.000 / 1.000.
\end{tablenotes}
\end{threeparttable}
\end{table}