\begin{table}[t]
\centering\small
\begin{threeparttable}
\caption{Empirical log-log slopes of the RMS scaled gap to $\widehat\theta_N$ against $m$ at fixed $N$ (largest $N$ of each design), with the slopes predicted by the leading bias term.}\label{tab:mc_rates}
\begin{tabular}{@{}llrrrrrrrrr@{}}
\toprule
Design & $p$ & $N$ & r1\_q0 & r1\_q1 & r1\_q2 & r2\_q0 & r2\_q1 & r3\_q0 & r3\_q1 & cs\_q1 \\
predicted & & & -1 & -2 & -4 & -2 & -4 & -3 & -6 & -4 \\
\midrule
exp & 1 & 4,194,304 & -1.01 & -2.03 & -4.05 & -1.39 & -2.61 & -0.89 & -1.69 & -1.05 \\
exp contam & 1 & 1,048,576 & -0.90 & -1.81 & -3.62 & -1.10 & -2.12 & -1.47 & -2.76 & -1.50 \\
logit & 3 & 1,048,576 & -1.02 & -2.05 & -4.16 & -1.15 & -2.29 & -2.28 & -6.32 & -1.01 \\
logit & 8 & 1,048,576 & -1.03 & -2.07 & -4.15 & -1.40 & -2.94 & -1.71 & -5.46 & -1.09 \\
logit misspec & 3 & 1,048,576 & -1.02 & -2.06 & -4.11 & -1.30 & -2.62 & -2.29 & -5.92 & -1.97 \\
logit p20 & 20 & 1,048,576 & -1.04 & -2.09 & -4.17 & -1.36 & -2.90 & -0.93 & -2.11 & -1.16 \\
pois & 3 & 1,048,576 & -1.02 & -2.04 & -4.15 & -1.22 & -2.78 & -1.96 & -3.98 & -1.07 \\
pois & 8 & 1,048,576 & -1.03 & -2.06 & -4.11 & -1.28 & -2.48 & -2.14 & -4.53 & -1.07 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\footnotesize
\item Slopes are least-squares fits over the available $m$ grid; they approach the predicted exponent only where the bias term dominates the random remainder and the sample is in the asymptotic regime. The predicted slope for the Cox--Snell + 1 Newton estimator assumes an exact first-order bias formula ($-4$). Source: \texttt{results/processed/summary.csv}.
\end{tablenotes}
\end{threeparttable}
\end{table}