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| "Theorem 4.2 establishes a central limit theorem for the empirical KL_inf statistic, showing sqrt(n)(KL_inf(q_hat_n, m_o) - KL_inf(q, m_o)) converges in distribution to N(0, sigma^2(q, m_o)) (Theorem 4.2).", | |
| "Theorem 4.4 extends this result to the stopping time tau_alpha, proving sqrt(log(1/alpha))(tau_alpha/log(1/alpha) - 1/KL_inf(q,m_o)) converges to a Gaussian limit N(0, sigma^2_bd(q,m_o)) as alpha to 0 (Theorem 4.4).", | |
| "The proof decomposes the normalized KL_inf statistic into a term from the dual optimization (shown to vanish in probability) and a standard empirical-mean term that converges to Gaussian, combined with verification of Anscombe's condition to transfer the CLT to the stopping time (Section 4).", | |
| "Proposition 4.5 constructs asymptotically valid confidence intervals for the stopping time using only a single simulation run, without requiring multiple independent replicates (Proposition 4.5).", | |
| "Numerical experiments on synthetic Beta and Bernoulli distributions and on real crop-yield data show empirical stopping-time distributions converging to the theoretical Gaussian limit, with stronger agreement at smaller significance levels alpha (Section 5)." | |
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