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arXiv · 2208.03185

Catoni-style Confidence Sequences under Infinite Variance

Sujay Bhatt·Guanhua Fang·Ping Li·Gennady Samorodnitsky
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Abstract

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~$p^{th}-$moment, where~$p \in (1,2]$, 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.

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Sujay Bhatt, Guanhua Fang, Ping Li, Gennady Samorodnitsky. 2022-08-05. Catoni-style Confidence Sequences under Infinite Variance. https://arxiv.org/abs/2208.03185

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