Merging sequential e-values via martingales

Vladimir Vovk, Ruodu Wang

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We study the problem of merging sequential or independent e-values into one e-value or e-process. We describe a class of e-value merging functions via martingales and show that it dominates all merging methods for sequential e-values. All admissible methods for constructing e-processes can also be obtained in this way. In the case of merging independent e-values, the situation becomes much more complicated, and we provide a general class of such merging functions based on martingales applied to reordered data.
Original languageEnglish
Pages (from-to)1185
Number of pages26
JournalElectronic Journal of Statistics
Issue number1
Publication statusAccepted/In press - 19 Feb 2024


  • anytime validity
  • betting scores
  • e-processes
  • admissibility
  • merging functions

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