Catoni-style Confidence Sequences under Infinite Variance

• URL: http://arxiv.org/abs/2208.03185v1
• Date: Fri, 5 Aug 2022 14:11:06 GMT
• Title: Catoni-style Confidence Sequences under Infinite Variance
• Authors: Sujay Bhatt and Guanhua Fang and Ping Li and Gennady Samorodnitsky
• Abstract summary: 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. The derived results are shown to better than confidence sequences obtained using Dubins-Savage inequality.
• Score: 19.61346221428679
• License: http://creativecommons.org/licenses/by/4.0/
• 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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