An exhaustive ADDIS principle for online FWER control

TL;DR

This paper introduces a uniform improvement to the ADDIS principle for online FWER control, enhancing hypothesis rejection power while maintaining error rate control, applicable to various ADDIS-based procedures.

Contribution

The authors propose a generalized ADDIS principle that improves power of existing procedures without losing FWER control, and demonstrate its application to ADDIS-Spending and ADDIS-Graph.

Findings

Improved ADDIS procedures reject more hypotheses while controlling FWER.

No other FWER procedure can enlarge the rejection event beyond the proposed method.

The new principle enhances existing ADDIS-based methods like ADDIS-Spending and ADDIS-Graph.

Abstract

In this paper we consider online multiple testing with familywise error rate (FWER) control, where the probability of committing at least one type I error shall remain under control while testing a possibly infinite sequence of hypotheses over time. Currently, Adaptive-Discard (ADDIS) procedures seem to be the most promising online procedures with FWER control in terms of power. Now, our main contribution is a uniform improvement of the ADDIS principle and thus of all ADDIS procedures. This means, the methods we propose reject as least as much hypotheses as ADDIS procedures and in some cases even more, while maintaining FWER control. In addition, we show that there is no other FWER controlling procedure that enlarges the event of rejecting any hypothesis. Finally, we apply the new principle to derive uniform improvements of the ADDIS-Spending and ADDIS-Graph.