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| \citation{deep2024asymptotically,deep2025asymptotic} |
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| \newlabel{fig:ber_clt@cref}{{[figure][2][]2}{[1][7][]7}{}{}{}} |
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| \newlabel{fig_tau_relaxed_beta}{{4}{8}{Histogram of the statistic $\sqrt {\log (1/\alpha )} ({\tau _{\alpha }}/{\log (1/\alpha )}-{1}/{\mathrm {KL}_{\inf }(q,m_o)})$ with $\alpha = 10^{-4}$ on left and $\alpha = 10^{-8}$ on right. The orange curve is the density of $\mathcal {N}\!\big (0,\ \sigma ^2_{\rm bd}(q,m_o)\big )$. The choice of $\beta (n,\alpha )$ is given in \eqref {eq:beta_const}}{figure.caption.4}{}} |
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| \newlabel{fig_real_data_set}{{5}{8}{Histogram of the statistic $\sqrt {\log (1/\alpha )} (\tau _{\alpha }/\log (1/\alpha )-1/\mathrm {KL}_{\inf }(\hat {q},m_o))$. The orange curve is the density of $\mathcal {N}\!\big (0,\ \hat {\sigma }^2_{\rm bd}(q,m_o)\big )$. The choice of $\beta (n,\alpha )$ is given in \eqref {eq:beta_const}}{figure.caption.5}{}} |
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| \newlabel{sec:discussion@cref}{{[section][6][]6}{[1][8][]8}{}{}{}} |
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| \bibcite{agrawal2021optimal}{{5}{2021{b}}{{Agrawal et~al.}}{{Agrawal, Koolen, and Juneja}}} |
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| \bibcite{billingsley2017probability}{{8}{2017}{{Billingsley}}{{}}} |
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| \bibcite{darling1967iterated}{{11}{1967}{{Darling \& Robbins}}{{Darling and Robbins}}} |
| \bibcite{deep2024asymptotically}{{12}{2024}{{Deep et~al.}}{{Deep, Bassamboo, and Juneja}}} |
| \bibcite{deep2025asymptotic}{{13}{2025}{{Deep et~al.}}{{Deep, Bassamboo, and Juneja}}} |
| \bibcite{fan2025fragility}{{14}{2025}{{Fan \& Glynn}}{{Fan and Glynn}}} |
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| \bibcite{honda2015non}{{17}{2015}{{Honda \& Takemura}}{{Honda and Takemura}}} |
| \bibcite{jourdan2022top}{{18}{2022}{{Jourdan et~al.}}{{Jourdan, Degenne, Baudry, de~Heide, and Kaufmann}}} |
| \bibcite{lai1985asymptotically}{{19}{1985}{{Lai \& Robbins}}{{Lai and Robbins}}} |
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| \newlabel{app:proof_lem:kl_inf_clt}{{A.1}{11}{Acknowledgements}{subsection.A.1}{}} |
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| \citation{billingsley2017probability} |
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| \citation{wang2026almost} |
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| \gdef \@abspage@last{33} |
| |
