arXiv Statistics ML By Chase Mathis, Ian Waudby-Smith

Confidence Horizons

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The paper introduces "confidence horizons", a new class of statistical tools that provide sharper large‑sample anytime‑valid inference when a finite time horizon is imposed. These objects function as large‑sample confidence sequences limited to a bounded number of interim looks, analogous to group sequential repeated confidence intervals. The authors connect confidence horizons to classic group sequential boundaries (Pocock, O’Brien–Fleming, Wang–Tsiatis), derive closed‑form distribution functions for certain statistics, and demonstrate their application to treatment effect estimation in sequentially randomized experiments with adaptive Neyman allocation.

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