Abstract

An e-value is a nonnegative random variable whose expected value is at most one under the null hypothesis. It is a fundamental concept in hypothesis testing, yet they have not been studied under a unified umbrella until about 5 years ago. Today, it is a fast-growing area of research. E-values are the fundamental building blocks for any-time valid inference but also turn out to provide some remarkable results besides sequential testing. We present a necessary and sufficient principle for multiple testing procedures controlling an expected loss, such as FDR. This principle asserts that every such multiple testing method is a special case of a general closed testing procedure based on e-values.

Based on joint work with Neil Xu, Aldo Solari, Lasse Fischer, Aaditya Ramdas, Jelle Goeman, Peter Grünwald and Wouter Koolen.