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

Tardivel, Patrick J.C.; Servien, Rémi; Concordet, Didier

Journal de la société française de statistique, Tome 162 (2021) no. 1, pp. 2-21.

Nous étudions le contrôle de la probabilité d’obtenir un ou plusieurs faux-positifs dans le cadre du modèle linéaire gaussien lorsque la matrice de planification $n\times p$ est de rang $p$. Les procédures de tests multiples non-séquentielles contrôlant cette probabilité sont dérivées de régions de confiance hyperrectangulaires. Dans cet article, nous construisons une procédure basée sur une région de confiance hyperrectangulaires de volume minimal. Nous montrons que la minimisation du volume est un critère judicieux pour augmenter la puissance d’une procédure de tests multiples. Des expériences numériques montrent que notre démarche fournit une procédure plus performante que les procédures séquentielles et non-séquentielles de l’état de l’art. Enfin, nous appliquons cette procédure à la détection de métabolites en métabolomique.

We study the control of the FamilyWise Error Rate (FWER) in the linear Gaussian model when the $n\times p$ 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 procedure derived from hyperrectangular confidence region 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.

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