# On Procedures Controlling the FDR for Testing Hierarchically Ordered Hypotheses

arXiv: https://arxiv.org/abs/1612.04467 · HTML: https://mlsanity.com/paper/1612.04467/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Dec 2016.

## Built on by (most cited first, 3 of 3)

- [Controlling the False Split Rate in Tree-Based Aggregation](https://mlsanity.com/paper/2108.05350/) (2021)
- [Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2109.11634/) (2021)
- [AdaPT-GMM: Powerful and robust covariate-assisted multiple testing](https://mlsanity.com/paper/2106.15812/) (2021)

## Abstract (arXiv)

Complex large-scale studies, such as those related to microarray data and fMRI studies, often involve testing multiple hierarchically ordered hypotheses. However, most existing false discovery rate (FDR) controlling procedures do not exploit the inherent hierarchical structure among the tested hypotheses. In this paper, we first present a generalized stepwise procedure which generalizes the usual stepwise procedure to the case where each hypothesis is tested with a different set of critical constants. This procedure is helpful in creating a general framework under which our hierarchical testing procedures are developed. Then, we present several hierarchical testing procedures which control the FDR under various forms of dependence such as positive dependence and block dependence. Our simulation studies show that these proposed methods can be more powerful in some situations than alternative methods such as Yekutieli's hierarchical testing procedure (Yekutieli, JASA 103 (2008) 309-316). Finally, we apply our proposed procedures to a real data set involving abundances of microbes in different ecological environments.