Nonparametric E-tests of Symmetry

Vovk, Vladimir; Wang, Ruodu

doi:10.51387/24-NEJSDS60

The New England Journal of Statistics in Data Science

Nonparametric E-tests of Symmetry

Volume 2, Issue 2 (2024), pp. 261–270

Vladimir Vovk Ruodu Wang

https://doi.org/10.51387/24-NEJSDS60

Pub. online: 23 February 2024 Type: Statistical Methodology

Open Access

Accepted
23 January 2023

Published
23 February 2024

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.

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Keywords

Hypothesis testing Nonparametric hypothesis testing E-values Pitman’s asymptotic relative efficiency

Funding

Vladimir Vovk’s research has been supported by Mitie. Ruodu Wang acknowledges financial support by grants CRC-2022-00141 and RGPIN-2018-03823 from the Natural Sciences and Engineering Research Council of Canada.

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