Abstract:We derive confidence intervals and confidence sequences for causal effects in situations where the back-door or front-door criteria are applicable. Our tightest confidence intervals hold in the standard setting where the training data consists of IID observations over a system described by a given causal diagram. When interventions are allowed to depend on the past data, our confidence intervals become wider and involve a term coming from the law of the iterated logarithm, even where the number of observations is known in advance. In the sequential setting where the number of observations is not given, our confidence intervals, arranged into a confidence sequence for causal effects, involve more iterated logarithm terms and become even wider.
| Comments: | 15 pages, 4 figures |
| Subjects: | Statistics Theory (math.ST) |
| MSC classes: | 62D20 (Primary) 62F25, 62G15, 62L12, 62M20, 93E35 (Secondary) |
| Cite as: | arXiv:2605.25687 [math.ST] |
| (or arXiv:2605.25687v1 [math.ST] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25687 arXiv-issued DOI via DataCite (pending registration) |
From: Vladimir Vovk [view email]
[v1]
Mon, 25 May 2026 10:41:24 UTC (14 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。