On Stopping Times of Power-one Sequential Tests: Tight Lower and Upper Bounds

Excerpt

arXiv:2504.19952v2 Announce Type: replace-cross Abstract: We present two general lower bounds for stopping times of sequential tests between arbitrary composite nulls $\mathcal P$ and alternatives $\mathcal Q$. The first lower bound is for the ``Wald setting'' where the type-1 error level $\alpha$ approaches zero for a fixed alternative $Q \in \mathcal Q$, and equals $\log(1/\alpha)$ divided by a certain infimum KL divergence between $\mathcal P$ and $Q$, termed $\operatorname{KL_{inf}}$. The se