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Sequential testing of conditionally constrained hypotheses
Eugenio Clerico · 2026-06-05 · via math.ST updates on arXiv.org

We explicitly characterise the full class of e-processes for testing conditional non-parametric hypotheses, defined by finitely many conditional constraints. Our main result is a complete-class theorem: every e-process for such a hypothesis is point-wise dominated by a predictable product of affine one-step e-variables. Therefore, for a broad class of conditional testing problems, arbitrary e-processes can be replaced without loss by test supermartingales. This extends previous complete-class results from single-step constrained testing and bounded one-dimensional conditional mean testing to a broader conditional sequential setting.

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