🤖 AI Summary
This work addresses the conservatism arising from the infinite-time validity assumption in sequential inference by introducing a “confidence horizon” framework that constructs anytime-valid confidence sequences within a finite time boundary. By integrating group sequential methods with adaptive Neyman allocation, the framework enables early stopping under budgetary or ethical constraints while preserving inferential accuracy. Key contributions include the first incorporation of a finite-time horizon into the anytime-valid inference paradigm, the establishment of explicit connections to classical group sequential boundaries (e.g., Pocock and O’Brien–Fleming), and the derivation of closed-form asymptotic quantiles that circumvent repeated integration. This analytical advance substantially improves the computational efficiency of critical value calculation and enhances the precision of treatment effect estimation.
📝 Abstract
Anytime-valid inference enables analysts to continuously monitor their data and stop experiments early. However, the majority of these methods incur a certain conservativeness by remaining valid on infinite time horizons. In practice, a bound on the horizon may be imposed due to budgetary, practical, or ethical constraints. In this paper, we ask the question: "Is it possible to obtain sharper large-sample anytime-valid inference by forgoing validity beyond some finite time horizon?". We provide a positive answer to this question by proposing a family of statistical objects that we call "confidence horizons". These objects can be viewed as large-sample confidence sequences on bounded time horizons, or alternatively as group sequential repeated confidence intervals with a maximal number of interim peeking times. We make explicit connections to the group sequential boundaries of Pocock [1977], O'Brien--Fleming [1979], and Wang--Tsiatis [1987]. We derive closed-form distribution functions of certain statistics which can be used to calculate the asymptotic quantiles of confidence horizons exactly, sidestepping the repeated integration typically employed in group sequential methods. We illustrate the use of confidence horizons for treatment effect estimation in sequentially randomized experiments under adaptive Neyman allocation.