Introduction to High-Dimensional Statistics, 2nd Edition

Chapter 10

Multiple Testing

DOI: 10.1201/9781003158745-10

In this chapter, we switch from the estimation problem to the test problem, and we explain some possible ways to handle the impact of high dimensionality in this context. More precisely, we will focus on the problem of performing simultaneously a large number of tests. This issue is of major importance in practice: Many scientific experiments seek to determine if a given factor has an impact on various quantities of interest. For example, we can seek for the possible side effects (headache, stomach pain, drowsiness, etc.) induced by a new drug. From a statistical perspective, this amounts to test simultaneously for each quantity of interest the hypothesis “the factor has no impact ...