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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 languageEnglish
Number of pages10
JournalNew England Journal of Statistics in Data Science
Early online date23 Feb 2024
Publication statusE-pub ahead of print - 23 Feb 2024


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

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