\begin{table}[p]
\centering\scriptsize
\begin{threeparttable}
\caption{Monte Carlo, logit design, $p = 8$, $N = 16,384$: scaled gap to $\widehat\theta_N$, scaled RMSE and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_p8}
\begin{tabular}{@{}lrrr@{}}
\toprule
Estimator & \multicolumn{3}{c}{$m = 256$, $K = 64$} \\
 & gap & RMSE & cov \\
\midrule
(1,0) plain average & 5.571 & 8.708 & 0.851 \\
(1,1) average + 1 Newton & 0.107 & 6.382 & 0.951 \\
(1,2) average + 2 Newton & 4.24e-5 & 6.388 & 0.952 \\
(2,0) half-block jackknife & 2.187 & 6.702 & 0.938 \\
(2,1) half-block + 1 Newton & 0.014 & 6.388 & 0.952 \\
(2,2) half-block + 2 Newton & 1.21e-6 & 6.388 & -- \\
(3,0) quarter-block & 2.992 & 7.046 & -- \\
(3,1) quarter-block + 1 Newton & 0.023 & 6.387 & 0.952 \\
analytic Cox--Snell + 1 Newton & 0.004 & 6.388 & 0.952 \\
CSL, 1 round & 0.802 & 6.420 & -- \\
CSL, 2 rounds & 0.253 & 6.405 & -- \\
AEE (Lin--Xi) & 5.091 & 7.946 & -- \\
(2,1) stale Hessian & 0.085 & 6.391 & -- \\
centralized MLE & 0 & 6.388 & 0.952 \\
\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.
\end{tablenotes}
\end{threeparttable}
\end{table}