Efficiency of nonparametric e-tests

TL;DR

This paper explores the use of e-values as an alternative to p-values in nonparametric symmetry testing, introducing new e-value analogues for popular tests and analyzing their efficiency.

Contribution

It introduces e-value analogues for three nonparametric tests of symmetry and proposes an asymptotic relative efficiency measure for e-values, expanding the theoretical framework.

Findings

E-value analogues for nonparametric symmetry tests are proposed.

An asymptotic relative efficiency measure for e-values is developed.

Limitations and future research directions are discussed.

Abstract

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.