Powerful multiple testing procedures derived from hyperrectangular confidence regions having a minimal volume

We study the control of the FamilyWise Error Rate (FWER) in the linear Gaussian model when the n × p design matrix is of rank p. Single step multiple testing procedures controlling the FWER are derived from hyperrectangular confidence regions. In this study, we aim to construct procedures derived from hyperrectangular confidence regions having a minimal volume. We show that minimizing the volume seems a fair criterion to improve the power of the multiple testing procedure. Numerical experiments demonstrate the performance of our approach when compared with the state-of-the-art single step and sequential procedures. We also provide an application to the detection of metabolites in metabolomics.