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

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  • Gnettner, Felix
  • Kirch, Claudia

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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  • Gnettner, Felix & Kirch, Claudia, 2025. "A new and flexible class of sharp asymptotic time-uniform confidence sequences," Statistics & Probability Letters, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:stapro:v:226:y:2025:i:c:s0167715225001075
    DOI: 10.1016/j.spl.2025.110462
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