# Online False Discovery Rate Control for LORD & SAFFRON Under Positive, Local Dependence

arXiv: https://arxiv.org/abs/2110.08161 · HTML: https://mlsanity.com/paper/2110.08161/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 15 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [Online Rules for Control of False Discovery Rate and False Discovery Exceedance](https://mlsanity.com/paper/1603.09000/) (2016)
- [Online control of the false discovery rate with decaying memory](https://mlsanity.com/paper/1710.00499/) (2017)
- [SAFFRON: an adaptive algorithm for online control of the false discovery rate](https://mlsanity.com/paper/1802.09098/) (2018)
- [Online Control of the False Coverage Rate and False Sign Rate](https://mlsanity.com/paper/1905.01059/) (2019)
- [ADDIS: an adaptive discarding algorithm for online FDR control with conservative nulls](https://mlsanity.com/paper/1905.11465/) (2019)
- [Conditional calibration for false discovery rate control under dependence](https://mlsanity.com/paper/2007.10438/) (2020)
- [Asynchronous Online Testing of Multiple Hypotheses](https://mlsanity.com/paper/1812.05068/) (2018)
- [Online control of the familywise error rate](https://mlsanity.com/paper/1910.04900/) (2019)
- [Contextual Online False Discovery Rate Control](https://mlsanity.com/paper/1902.02885/) (2019)
- [The Power of Batching in Multiple Hypothesis Testing](https://mlsanity.com/paper/1910.04968/) (2019)
- [PAPRIKA: Private Online False Discovery Rate Control](https://mlsanity.com/paper/2002.12321/) (2020)
- [Dynamic Algorithms for Online Multiple Testing](https://mlsanity.com/paper/2010.13953/) (2020)

## Built on by (most cited first, 1 of 1)

- [Online multiple testing with e-values](https://mlsanity.com/paper/2311.06412/) (2023)

## Abstract (arXiv)

Online testing procedures assume that hypotheses are observed in sequence, and allow the significance thresholds for upcoming tests to depend on the test statistics observed so far. Some of the most popular online methods include alpha investing, LORD++ (hereafter, LORD), and SAFFRON. These three methods have been shown to provide online control of the "modified" false discovery rate (mFDR) under a condition known as conditional superuniformity. However, to our knowledge, LORD & SAFFRON have only been shown to control the traditional false discovery rate (FDR) under an independence condition on the test statistics. Our work bolsters these results by showing that SAFFRON and LORD additionally ensure online control of the FDR under a "local" form of nonnegative dependence. Further, FDR control is maintained under certain types of adaptive stopping rules, such as stopping after a certain number of rejections have been observed. Because alpha investing can be recovered as a special case of the SAFFRON framework, our results immediately apply to alpha investing as well. In the process of deriving these results, we also formally characterize how the conditional superuniformity assumption implicitly limits the allowed p-value dependencies. This implicit limitation is important not only to our proposed FDR result, but also to many existing mFDR results.