Catoni-style Confidence Sequences under Infinite Variance
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Abstract (arXiv)
In this paper, we provide an extension of confidence sequences for settings where the variance of the data-generating distribution does not exist or is infinite. Confidence sequences furnish confidence intervals that are valid at arbitrary data-dependent stopping times, naturally having a wide range of applications. We first establish a lower bound for the width of the Catoni-style confidence sequences for the finite variance case to highlight the looseness of the existing results. Next, we derive tight Catoni-style confidence sequences for data distributions having a relaxed bounded~pth-moment, where~p ∈ (1,2], and strengthen the results for the finite variance case of~p =2. The derived results are shown to better than confidence sequences obtained using Dubins-Savage inequality.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 5 of its 17 references that are in the map. First posted on arXiv 5 Aug 2022.
Builds on
5 of 17 references.
References · 5
- 2018Time-uniform, nonparametric, nonasymptotic confidence sequencescited by 220
- 2020Estimating means of bounded random variables by bettingcited by 164
- 2021Off-Policy Evaluation via Adaptive Weighting with Data from Contextual Banditscited by 40
- 2015Always Valid Inference: Bringing Sequential Analysis to A/B Testingcited by 20
- 2022Catoni-style confidence sequences for heavy-tailed mean estimationcited by 17
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Citing papers per year: 2023: 1; 2024: 0; 2025: 1.
2 papers.