Papers › Improving Wald's (approximate) sequential probability ratio test by avoiding overshoot
Improving Wald's (approximate) sequential probability ratio test by avoiding overshoot
Lasse Fischer, Aaditya Ramdas
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Wald's sequential probability ratio test (SPRT) is a cornerstone of sequential analysis. Based on desired type-I, II error levels α, β, it stops when the likelihood ratio crosses certain thresholds, guaranteeing optimality of the expected sample size. However, these thresholds are not closed form and the test is often applied with approximate thresholds (1-β)/α and β/(1-α) (approximate SPRT). When β> 0, this neither guarantees error control at α,β nor optimality. When β=0 (power-one SPRT), this method is conservative and not optimal. The looseness in both cases is caused by \emph{overshoot}: the test statistic overshoots the thresholds at the stopping time. Numerically calculating thresholds may be infeasible, and most software packages do not do this. We improve the approximate SPRT by modifying the test statistic to avoid overshoot. Our `sequential boosting' technique uniformly improves power-one SPRTs (β=0) for simple nulls and alternatives, or for one-sided nulls and alternatives in exponential families. When β> 0, our techniques provide guaranteed error control at α,β, while needing less samples than the approximate SPRT in our simulations. We also provide several nontrivial extensions: confidence sequences, sampling without replacement and conformal martingales.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections