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| "stopping_time_gaussian_fit_improves": true, |
| "zero_lambda_control_destroys_signal": true |
| }, |
| "paper_id": "HMyCBL2yMV", |
| "paper_title": "Beyond First-order Asymptotics in Sequential Mean Testing", |
| "claims": [ |
| {"claim": 1, "literal_claim": "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)."}, |
| {"claim": 2, "literal_claim": "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)."}, |
| {"claim": 3, "literal_claim": "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)."}, |
| {"claim": 4, "literal_claim": "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)."}, |
| {"claim": 5, "literal_claim": "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)."} |
| ], |
| "seed": 260604520, |
| "source_checks": { |
| "arxiv-2606.04520.pdf": true, |
| "arxiv-2606.04520.tar": true, |
| "dssat-maize-a4f95d3.tar.gz": true, |
| "icml_final_submission.tex": true |
| }, |
| "source_literals": { |
| "beta_distribution": true, |
| "dssat": true, |
| "single_path": true, |
| "stopping_rule": true, |
| "theory_boundary": true |
| } |
| } |
|
|
