Testing the mean and variance by e-processes

Yixuan Fan, Zhanyi Jiao and Ruodu Wang

Biometrika, 2025, vol. 112, issue 1, 289-300

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.

Keywords: E-process; E-value; P-value; Symmetry; Unimodality (search for similar items in EconPapers)
Date: 2025
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