# Online Control of the False Coverage Rate and False Sign Rate

arXiv: https://arxiv.org/abs/1905.01059 · HTML: https://mlsanity.com/paper/1905.01059/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2019.

## Built on by (most cited first, 11 of 11)

- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Derandomized Novelty Detection with FDR Control via Conformal E-values](https://mlsanity.com/paper/2302.07294/) (2023)
- [Confidence on the Focal: Conformal Prediction with Selection-Conditional Coverage](https://mlsanity.com/paper/2403.03868/) (2024)
- [Online multiple testing with e-values](https://mlsanity.com/paper/2311.06412/) (2023)
- [Error-quantified Conformal Inference for Time Series](https://mlsanity.com/paper/2502.00818/) (2025)
- [Conformal Selective Acting: Anytime-Valid Risk Control for RLVR-Trained LLMs](https://mlsanity.com/paper/2605.20270/) (2026)
- [Selecting informative conformal prediction sets with false coverage rate control](https://mlsanity.com/paper/2403.12295/) (2024)
- [Online Selective Conformal Prediction: Errors and Solutions](https://mlsanity.com/paper/2503.16809/) (2025)
- [Online Control of the False Discovery Rate under "Decision Deadlines"](https://mlsanity.com/paper/2110.01583/) (2021)
- [Online False Discovery Rate Control for LORD & SAFFRON Under Positive, Local Dependence](https://mlsanity.com/paper/2110.08161/) (2021)
- [Spawn Freely, Act Sparingly: Progressive Risk Vesting for Recursive LLM-Agent Trees](https://mlsanity.com/paper/2609.01035/) (2026)

## Abstract (arXiv)

The false coverage rate (FCR) is the expected ratio of number of constructed confidence intervals (CIs) that fail to cover their respective parameters to the total number of constructed CIs. Procedures for FCR control exist in the offline setting, but none so far have been designed with the online setting in mind. In the online setting, there is an infinite sequence of fixed unknown parameters θt ordered by time. At each step, we see independent data that is informative about θt, and must immediately make a decision whether to report a CI for θt or not. If θt is selected for coverage, the task is to determine how to construct a CI for θt such that FCR ≤ α for any T∈ mathbbN. A straightforward solution is to construct at each step a (1-α) level conditional CI. In this paper, we present a novel solution to the problem inspired by online false discovery rate (FDR) algorithms, which only requires the statistician to be able to construct a marginal CI at any given level. Apart from the fact that marginal CIs are usually simpler to construct than conditional ones, the marginal procedure has an important qualitative advantage over the conditional solution, namely, it allows selection to be determined by the candidate CI itself. We take advantage of this to offer solutions to some online problems which have not been addressed before. For example, we show that our general CI procedure can be used to devise online sign-classification procedures that control the false sign rate (FSR). In terms of power and length of the constructed CIs, we demonstrate that the two approaches have complementary strengths and weaknesses using simulations. Last, all of our methodology applies equally well to online FCR control for prediction intervals, having particular implications for assumption-free selective conformal inference.