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Testing the mean and variance by e-processes

Author

Listed:
  • Yixuan Fan
  • Zhanyi Jiao
  • Ruodu Wang

Abstract

SummaryWe address the problem of testing the conditional mean and conditional variance for nonstationary data. We build e-values and p-values for four types of nonparametric composite hypothesis with specified mean and variance as well as other conditions on the shape of the data-generating distribution. These shape conditions include symmetry, unimodality and their combination. Using the obtained e-values and p-values, we construct tests via e-processes, also known as testing by betting, as well as some tests based on combining p-values for comparison. Although we mainly focus on one-sided tests, the two-sided test for the mean is also studied. Simulation and empirical studies are conducted under a few settings, and they illustrate features of the methods based on e-processes.

Suggested Citation

  • Yixuan Fan & Zhanyi Jiao & Ruodu Wang, 2025. "Testing the mean and variance by e-processes," Biometrika, Biometrika Trust, vol. 112(1), pages 289-300.
    • Handle: RePEc:oup:biomet:v:112:y:2025:i:1:p:289-300.
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    File URL: http://hdl.handle.net/10.1093/biomet/asae049
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