# On Stepwise Control of Directional Errors under Independence and Some Dependence

arXiv: https://arxiv.org/abs/1602.02854 · HTML: https://mlsanity.com/paper/1602.02854/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2016.

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

- [Selecting informative conformal prediction sets with false coverage rate control](https://mlsanity.com/paper/2403.12295/) (2024)

## Abstract (arXiv)

In this paper, the problem of error control of stepwise multiple testing procedures is considered. For two-sided hypotheses, control of both type 1 and type 3 (or directional) errors is required, and thus mixed directional familywise error rate control and mixed directional false discovery rate control are each considered by incorporating both types of errors in the error rate. Mixed directional familywise error rate control of stepwise methods in multiple testing has proven to be a challenging problem, as demonstrated in Shaffer (1980). By an appropriate formulation of the problem, some new stepwise procedures are developed that control type 1 and directional errors under independence and various dependencies.