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

• URL: http://arxiv.org/abs/2502.10380v1
• Date: Fri, 14 Feb 2025 18:57:16 GMT
• Title: A new and flexible class of sharp asymptotic time-uniform confidence sequences
• Authors: Felix Gnettner, Claudia Kirch,
• Abstract summary: As in classical statistics, confidence sequences are a nonparametric tool showing under which high-level assumptions coverage is achieved. We propose a new flexible class of confidence sequences yielding sharp time-uniform confidence sequences under mild assumptions.
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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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