{"ID":3052348,"CreatedAt":"2026-06-04T04:41:36.695875263Z","UpdatedAt":"2026-06-06T06:50:57.632975493Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04520","arxiv_id":"2606.04520","title":"Beyond First-order Asymptotics in Sequential Mean Testing","abstract":"We revisit the problem of sequentially testing the mean of bounded distributions in a level-$α$ power-one framework. We study a $\\mathrm{KL_{inf}}$-based sequential test that is known to attain the information-theoretic lower bound on the expected stopping time with exact constants as $α\\to 0$. Going beyond first-order asymptotics, we establish a central limit theorem (CLT) for the stopping time of this test. Our analysis proceeds in two steps. First, we prove a novel CLT for the $\\mathrm{KL_{inf}}$ statistic itself, characterizing its fluctuations around its deterministic limit. We then leverage this result to show that the stopping time, centered appropriately and scaled by $\\sqrt{\\log(1/α)}$, converges in distribution to a Gaussian limit with an explicit variance. This yields a second-order characterization of an asymptotically optimal sequential test for bounded distributions. Finally, we present numerical experiments that corroborate our theoretical findings.","short_abstract":"We revisit the problem of sequentially testing the mean of bounded distributions in a level-$α$ power-one framework. We study a $\\mathrm{KL_{inf}}$-based sequential test that is known to attain the information-theoretic lower bound on the expected stopping time with exact constants as $α\\to 0$. Going beyond first-order...","url_abs":"https://arxiv.org/abs/2606.04520","url_pdf":"https://arxiv.org/pdf/2606.04520v1","authors":"[\"Vikas Deep\",\"Shubhada Agrawal\"]","published":"2026-06-03T06:56:15Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\"]","methods":"[]","has_code":false}