Asymptotically Lossless Exact and Pivotal E-Values

Hengzhi He; Guang Cheng

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arXiv · 2609.27923

Asymptotically Lossless Exact and Pivotal E-Values

Hengzhi He·Guang Cheng

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Abstract

Consider testing a finite composite null $\cP={P_1,\ldots,P_L}$ against a simple alternative $Q$ using $n$ i.i.d. observations. Let $\ell_n$ denote the supremum of the expected log e-value over e-variables that are exact under every $P_i$ and pivotal across the nulls. Zhang, Ramdas, and Wang (2024) showed that $\ell_n$ is superadditive and asked whether $\ell_n/n$ converges to the upper bound $\min_i D(Q|P_i)$ under their joint atomlessness and absolute continuity assumptions. We prove that it does. The proof draws on techniques developed by Zhang, Ramdas, and Wang (2024) and by Farooq, Fritz, Haapasalo, and Tomamichel (2024).

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Hengzhi He, Guang Cheng. 2026-08-21. Asymptotically Lossless Exact and Pivotal E-Values. https://arxiv.org/abs/2609.27923

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