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.

翻译：e值概念最近被提出，作为统计假设检验中临界区域和p值的可能替代方案。本文考虑对称性非参数假设的检验，引入三种常见非参数检验的e值对应形式，定义e值的Pitman渐近相对效率对应概念，并将其应用于这三种非参数检验。我们讨论了渐近相对效率简单定义的局限性，并列举了进一步研究的方向。