FDP control in mass-univariate linear models using the residual bootstrap

In this article we develop a method for performing post hoc inference of the False Discovery Proportion (FDP) over multiple contrasts of interest in the mass-univariate linear model. To do so we use the residual bootstrap to simulate from the distribution of the null contrasts. We combine the bootstrap with the post hoc inference bounds of [11] and prove that doing so provides simultaneous asymptotic control of the FDP over all subsets of hypotheses. We demonstrate, via simulations, that our approach provides simultaneous control of the FDP over all subsets and is typically more powerful than existing, state of the art, parametric methods. We illustrate our approach on functional Magnetic Resonance Imaging data from the Human Connectome project and on a transcriptomic dataset of chronic obstructive pulmonary disease.