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Asymptotically Lossless Exact and Pivotal E-Values
Abstract
Consider testing a finite composite null cP=P1,…,PL against a simple alternative Q using n i.i.d. observations. Let ℓn denote the supremum of the expected log e-value over e-variables that are exact under every Pi and pivotal across the nulls. Zhang, Ramdas, and Wang (2024) showed that ℓn is superadditive and asked whether ℓn/n converges to the upper bound mini D(Q|Pi) 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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BibTeX
@misc{he2026asymptotically,
title = {{Asymptotically Lossless Exact and Pivotal E-Values}},
author = {Hengzhi He and Guang Cheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27923},
eprint = {2609.27923},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27923},
}
RIS
TY - UNPB
TI - Asymptotically Lossless Exact and Pivotal E-Values
AU - Hengzhi He
AU - Guang Cheng
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27923
UR - https://arxiv.org/abs/2609.27923
AB - Consider testing a finite composite null cP=P_1,…,P_L against a simple alternative Q using n i.i.d. observations. Let ℓ_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 ℓ_n is superadditive and asked whether ℓ_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).
ER -