Minimax regret and monotone optimality in multiple testing
Abstract
Confirmatory trials may seek efficacy claims in a prespecified subgroup and the full popu- lation, although benefit outside the subgroup is uncertain. We measure power loss relative to the marginal level-α test available if the population to protect were known, using the same experiment. In a bivariate Gaussian model with known covariance, we minimise the largest power loss, or regret, over prespecified ranges of target and non-target effects, subject to strong familywise error control and coordinatewise monotonicity. We optimise over monotone closed- testing procedures with fixed marginal tests, allowing randomisation in the shared intersection test. Monotonicity places the worst non-target mean at its lower planning bound for each target effect. On the resulting reduced planning set, every least-favourable distribution is supported on exactly two efficacy scenarios, one for each target population. Under a condition on the effect ranges and covariance, the minimax procedure is nonrandomised and unique up to null sets. An integral criterion characterises exactly when a calibrated step-up procedure attains the minimax value within this class. Bounds for the continuous problem quantify possible improve- ments over simple procedures. An asthma planning example illustrates power allocation and the compatibility of target assignments with treatment benefits and burdens.
Related
- Simple-regret rates and minimax optimality of fixed-prior expected improvement in Matérn and squared-exponential RKHSs
- Bandits with Multiple Optimal Arms: Minimax Regret and Non-Adaptivity
- Expected Minimax Regret Rates for Adaptive LQG Control on Fixed Parameter Sets
- Towards instance-dependent regret optimality in Episodic MDPs with Posterior Sampling
- Exact Bayes Regret and Asymptotic Optimality in High-Dimensional Gaussian Bandits
BibTeX
@misc{li2026minimax,
title = {{Minimax regret and monotone optimality in multiple testing}},
author = {Lei Li and Yuexiao Dong},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03155},
eprint = {2611.03155},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03155},
}
RIS
TY - UNPB
TI - Minimax regret and monotone optimality in multiple testing
AU - Lei Li
AU - Yuexiao Dong
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03155
UR - https://arxiv.org/abs/2611.03155
AB - Confirmatory trials may seek efficacy claims in a prespecified subgroup and the full popu- lation, although benefit outside the subgroup is uncertain. We measure power loss relative to the marginal level-α test available if the population to protect were known, using the same experiment. In a bivariate Gaussian model with known covariance, we minimise the largest power loss, or regret, over prespecified ranges of target and non-target effects, subject to strong familywise error control and coordinatewise monotonicity. We optimise over monotone closed- testing procedures with fixed marginal tests, allowing randomisation in the shared intersection test. Monotonicity places the worst non-target mean at its lower planning bound for each target effect. On the resulting reduced planning set, every least-favourable distribution is supported on exactly two efficacy scenarios, one for each target population. Under a condition on the effect ranges and covariance, the minimax procedure is nonrandomised and unique up to null sets. An integral criterion characterises exactly when a calibrated step-up procedure attains the minimax value within this class. Bounds for the continuous problem quantify possible improve- ments over simple procedures. An asthma planning example illustrates power allocation and the compatibility of target assignments with treatment benefits and burdens.
ER -