Hypothesis testing with e-values

TL;DR

This book provides a comprehensive and unified overview of e-values in hypothesis testing, covering fundamental concepts, core ideas, and advanced topics, integrating recent research and unpublished results.

Contribution

It offers the first unified, detailed treatment of e-values, consolidating modern research and introducing new results in hypothesis testing methodology.

Findings

Collates important results from modern papers on e-values

Includes many results not published elsewhere

Provides a coherent overview of a fast-growing research area

Abstract

This book is written to offer a humble, but unified, treatment of e-values in hypothesis testing. It is organized into three parts: Fundamental Concepts, Core Ideas, and Advanced Topics. The first part includes four chapters that introduce the basic concepts. The second part includes five chapters of core ideas such as universal inference, log-optimality, e-processes, operations on e-values, and e-values in multiple testing. The third part contains seven chapters of advanced topics. The book collates important results from a variety of modern papers on e-values and related concepts, and also contains many results not published elsewhere. It offers a coherent and comprehensive picture on a fast-growing research area, and is ready to use as the basis of a graduate course in statistics and related fields.