A new and flexible class of sharp asymptotic time-uniform confidence sequences

Felix Gnettner; Claudia Kirch

doi:10.1016/j.spl.2025.110462

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arXiv · 2502.10380

A new and flexible class of sharp asymptotic time-uniform confidence sequences

Felix Gnettner·Claudia Kirch

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Abstract

Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences are a nonparametric tool showing under which high-level assumptions asymptotic coverage is achieved so that they also give a certain robustness guarantee against distributional deviations. In this paper, we propose a new flexible class of confidence sequences yielding sharp asymptotic time-uniform confidence sequences under mild assumptions. Furthermore, we highlight the connection to corresponding sequential testing problems and detail the underlying limit theorem.

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Felix Gnettner, Claudia Kirch. 2025-02-14. A new and flexible class of sharp asymptotic time-uniform confidence sequences. https://doi.org/10.1016/j.spl.2025.110462

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