Simultaneous high-probability bounds on the false discovery proportion in structured, regression, and online settings

Understand

While traditional multiple testing procedures prohibit adaptive analysis choices made by users, Goeman and Solari (2011) proposed a simultaneous inference framework that allows users such flexibility while preserving high-probability bounds on the false discovery proportion (FDP) of the chosen set.

• In this paper, we propose a new class of such simultaneous FDP bounds, tailored for nested sequences of rejection sets.
• While most existing simultaneous FDP bounds are based on closed testing using global null tests based on sorted p-values, we additionally consider the setting where side information can be leveraged to boost power, the variable selection setting where knockoff statistics can be used to order variables, and the online setting where decisions about rejections must be made as data arrives.
• Our finite-sample, closed form bounds are based on repurposing the FDP estimates from false discovery rate (FDR) controlling procedures designed for each of the above settings.