The New England Journal of Statistics in Data Science

The notion of an e-value has been recently proposed as a possible alternative to critical regions and p-values in statistical hypothesis testing. In this paper we consider testing the nonparametric hypothesis of symmetry, introduce analogues for e-values of three popular nonparametric tests, define an analogue for e-values of Pitman’s asymptotic relative efficiency, and apply it to the three nonparametric tests. We discuss limitations of our simple definition of asymptotic relative efficiency and list directions of further research.

We highlight points of agreement between Meng’s suggested principles and those proposed in our 2019 editorial in The American Statistician. We also discuss some questions that arise in the application of Meng’s principles in practice.