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

Felix Gnettner and Claudia Kirch

Statistics & Probability Letters, 2025, vol. 226, issue C

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.

Keywords: Anytime-valid inference; Time-uniform confidence sequence; Nonparametric; Sequential testing (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110462

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