\begin{table}[p]
\centering\scriptsize\setlength{\tabcolsep}{2.6pt}
\begin{threeparttable}
\caption{Monte Carlo, logit small m design, $p = 8$, $N = 262,144$: scaled gap to $\widehat\theta_N$ (root mean square and median) and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_small_m_p8}
\begin{tabular}{@{}lrrrrrr@{}}
\toprule
Estimator & \multicolumn{3}{c}{$m = 16$, $K = 16,384$} & \multicolumn{3}{c}{$m = 32$, $K = 8,192$} \\
 & gap & median & cov & gap & median & cov \\
\midrule
(1,0) plain average & 1.12e+5 & 4.63e+4 & 0.000 & 1.35e+4 & 9069.927 & 0.000 \\
(1,1) average + 1 Newton & 2.29e+11 & 5.70e+7 & 0.952 & 8.80e+7 & 4.90e+5 & 0.009 \\
(1,2) average + 2 Newton & -- & 9.09e+17 & -- & 2.70e+26 & 2.08e+11 & 0.028 \\
(2,0) half-block jackknife & 2.35e+5 & 8.92e+4 & 0.000 & 2.06e+5 & 2.96e+4 & 0.001 \\
(2,1) half-block + 1 Newton & 1.78e+12 & 4.03e+8 & 0.586 & 3.25e+12 & 4.36e+7 & 0.667 \\
(2,2) half-block + 2 Newton & -- & 1.69e+25 & -- & 1.98e+61 & 7.59e+16 & -- \\
(3,0) quarter-block & 5.44e+35 & 3.54e+21 & -- & 4.14e+5 & 6.85e+4 & -- \\
(3,1) quarter-block + 1 Newton & 5.44e+35 & 3.54e+21 & 0.000 & 3.24e+13 & 5.53e+8 & 0.539 \\
(2,1) valid workers only & 1.21e+5 & 8.00e+4 & -- & 80.687 & 80.697 & -- \\
(3,1) valid workers only & 5.44e+35 & 3.54e+21 & -- & 1.91e+4 & 1.09e+4 & -- \\
analytic Cox--Snell + 1 Newton & 6.41e+23 & 6.36e+18 & -- & -- & 7.37e+12 & -- \\
CSL, 1 round & -- & 6.93e+14 & -- & 1.38e+14 & 558.363 & -- \\
CSL, 2 rounds & -- & 2.41e+15 & -- & 3.39e+15 & 745.948 & -- \\
AEE (Lin--Xi) & 302.535 & 302.525 & -- & 168.888 & 168.867 & -- \\
(2,1) stale Hessian & 2.33e+5 & 8.64e+4 & -- & 2.05e+5 & 2.67e+4 & -- \\
centralized MLE & 0 & -- & 0.947 & 0 & -- & 0.947 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\footnotesize
\item 500 paired replications per column. gap $=$ root mean square of $\sqrt N\,\lVert\tilde\theta - \widehat\theta_N\rVert$ 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 $\approx 0.010$ or less.
\item Fraction of workers with all local fits valid (orders 2 / 3): $m=16$: 0.304 / 0.000; $m=32$: 0.094 / 0.092. 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.
\end{tablenotes}
\end{threeparttable}
\end{table}