Nonparametric e-tests of symmetry

Vladimir Vovk; Ruodu Wang

doi:10.51387/24-NEJSDS60

Nonparametric e-tests of symmetry

Vladimir Vovk, Ruodu Wang

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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.

Original language	English
Number of pages	10
Journal	New England Journal of Statistics in Data Science
Early online date	23 Feb 2024
DOIs	https://doi.org/10.51387/24-NEJSDS60
Publication status	E-pub ahead of print - 23 Feb 2024

Keywords

hypothesis testing
nonparametric hypothesis testing
e-values
Pitman's asymptotic relative efficiency

Access to Document

10.51387/24-NEJSDS60Licence: CC BY

Final published versionFinal published version, 340 KBLicence: CC BY

https://arxiv.org/abs/2208.08925

Cite this

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AB - 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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