\begin{table}[p]
\centering\scriptsize\setlength{\tabcolsep}{2.6pt}
\begin{threeparttable}
\caption{Monte Carlo, logit misspec design, $p = 3$, $N = 1,048,576$: scaled gap to $\widehat\theta_N$ (root mean square and median) and 95\% coverage by local sample size $m$.}\label{tab:mc_logit_misspec_p3}
\begin{tabular}{@{}lrrrrrrrrrrrr@{}}
\toprule
Estimator & \multicolumn{3}{c}{$m = 32$, $K = 32,768$} & \multicolumn{3}{c}{$m = 64$, $K = 16,384$} & \multicolumn{3}{c}{$m = 256$, $K = 4,096$} & \multicolumn{3}{c}{$m = 512$, $K = 2,048$} \\
 & gap & median & cov & gap & median & cov & gap & median & cov & gap & median & cov \\
\midrule
(1,0) plain average & 132.943 & 120.766 & 0.234 & 52.067 & 52.014 & 0.313 & 12.064 & 12.056 & 0.339 & 5.968 & 5.971 & 0.656 \\
(1,1) average + 1 Newton & 9.239 & 5.147 & 0.679 & 0.902 & 0.899 & 0.947 & 0.047 & 0.047 & 0.951 & 0.011 & 0.011 & 0.944 \\
(1,2) average + 2 Newton & 0.153 & 0.009 & 0.940 & 2.66e-4 & 2.63e-4 & 0.951 & 7.15e-7 & 7.08e-7 & 0.951 & 4.26e-8 & 4.20e-8 & 0.944 \\
(2,0) half-block jackknife & 7211.550 & 6132.656 & 0.001 & 42.709 & 16.900 & 0.262 & 0.879 & 0.765 & 0.944 & 0.476 & 0.416 & 0.944 \\
(2,1) half-block + 1 Newton & 2.32e+6 & 7.19e+4 & 0.001 & 1.992 & 0.090 & 0.939 & 2.93e-4 & 1.47e-4 & 0.951 & 7.54e-5 & 3.69e-5 & 0.944 \\
(2,2) half-block + 2 Newton & 1.65e+15 & 7.43e+7 & -- & 0.012 & 2.65e-6 & -- & 5.96e-11 & 5.76e-12 & -- & 5.86e-12 & 5.55e-12 & -- \\
(3,0) quarter-block & 1.20e+4 & 4193.362 & -- & 2756.874 & 2019.275 & -- & 0.990 & 0.856 & -- & 0.643 & 0.574 & -- \\
(3,1) quarter-block + 1 Newton & 4.77e+7 & 2.12e+4 & 0.007 & 1.99e+5 & 3127.163 & 0.001 & 3.15e-4 & 1.54e-4 & 0.951 & 1.31e-4 & 6.72e-5 & 0.944 \\
(2,1) valid workers only & 4.293 & 4.289 & -- & 0.083 & 0.082 & -- & -- & -- & -- & -- & -- & -- \\
(3,1) valid workers only & 3.797 & 3.757 & -- & 0.031 & 0.027 & -- & -- & -- & -- & -- & -- & -- \\
analytic Cox--Snell + 1 Newton & 2.43e+18 & 0.093 & 0.719 & 0.021 & 0.021 & 0.950 & 0.001 & 0.001 & 0.951 & 3.26e-4 & 3.09e-4 & 0.944 \\
CSL, 1 round & 46.770 & 32.852 & -- & 12.464 & 10.192 & -- & 1.379 & 1.221 & -- & 0.464 & 0.395 & -- \\
CSL, 2 rounds & 43.714 & 13.394 & -- & 5.971 & 2.651 & -- & 0.264 & 0.158 & -- & 0.059 & 0.035 & -- \\
AEE (Lin--Xi) & 80.781 & 80.780 & -- & 41.702 & 41.692 & -- & 10.841 & 10.840 & -- & 5.470 & 5.473 & -- \\
(2,1) stale Hessian & 4713.927 & 3228.813 & -- & 5.269 & 1.103 & -- & 0.013 & 0.011 & -- & 0.004 & 0.003 & -- \\
centralized MLE & 0 & -- & 0.941 & 0 & -- & 0.951 & 0 & -- & 0.951 & 0 & -- & 0.944 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\footnotesize
\item 500/500/1000/1000/1000 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): $m=32$: 0.972 / 0.268; $m=64$: 1.000 / 0.945; $m=128$: 1.000 / 1.000; $m=256$: 1.000 / 1.000; $m=512$: 1.000 / 1.000. 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}