# Catoni-style Confidence Sequences under Infinite Variance

arXiv: https://arxiv.org/abs/2208.03185 · HTML: https://mlsanity.com/paper/2208.03185/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 17 references that are in the map.
- First posted on arXiv 5 Aug 2022.

## Builds on (most cited first, 5 of 5)

- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Off-Policy Evaluation via Adaptive Weighting with Data from Contextual Bandits](https://mlsanity.com/paper/2106.02029/) (2021)
- [Always Valid Inference: Bringing Sequential Analysis to A/B Testing](https://mlsanity.com/paper/1512.04922/) (2015)
- [Catoni-style confidence sequences for heavy-tailed mean estimation](https://mlsanity.com/paper/2202.01250/) (2022)

## Built on by (most cited first, 2 of 2)

- [Risk-limiting Financial Audits via Weighted Sampling without Replacement](https://mlsanity.com/paper/2305.06884/) (2023)
- [Catoni-Style Change Point Detection for Regret Minimization in Non-Stationary Heavy-Tailed Bandits](https://mlsanity.com/paper/2505.20051/) (2025)

## 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.