Hypothesis testing with e-values
arXiv:2410.23614 · doi:10.1561/3600000002
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.
Published in: Foundations and Trends in Statistics, Vol. 1: No. 1-2, pp 1-390
References in corpus (15)
- Higher order elicitability and Osband's principle
- General maximum likelihood empirical Bayes estimation of normal means
- Hypothesis test for normal mixture models: The EM approach
- Time-uniform, nonparametric, nonasymptotic confidence sequences
- Test Martingales, Bayes Factors and -Values
- Two simple sufficient conditions for FDR control
- Testing randomness
- Sequential estimation of quantiles with applications to A/B-testing and best-arm identification
- Catoni-style confidence sequences for heavy-tailed mean estimation
- Confidence and discoveries with e-values
- Martingale Methods for Sequential Estimation of Convex Functionals and Divergences
- Sums of Standard Uniform Random Variables
- Post-selection inference for e-value based confidence intervals
- Combining exchangeable p-values
- Anytime valid and asymptotically optimal inference driven by predictive recursion