Adaptive confidence intervals with missing data
Abstract
We consider the construction of confidence intervals for population means when observations are subject to missingness. To accommodate more general missingness mechanisms than missing completely at random (MCAR), we adopt a reparametrised version of the realisable contamination model of Ma et al. (2026), which is a mixture of an MCAR version and a missing not at random version of the same base distribution P. We characterise the minimax length of confidence intervals that can adapt to potentially unknown parameters of the model, including the contamination fraction, for Gaussian base distributions and for nonparametric classes satisfying certain tail or symmetry assumptions. In all of these settings, we provide explicit constructions of simple, practical and finite-sample valid adaptive confidence intervals that attain the corresponding minimax rates. Finally, we provide implications of our results for causal inference.
Related
- Robustness intervals for competing risks analysis with causes of failure missing not at random
- Confidence Intervals Based on the Modified Chi-Squared Distribution and Its Applications in Medicine
- Changepoint localization via nested exchangeability tests: from point estimates to confidence intervals
- Sub-Gaussian Confidence Intervals for Heavy-Tailed Data: Characterizing the Limits of Inference
- Differentially Private Confidence Intervals for Relative Risk and Odds Ratio
BibTeX
@misc{ma2026adaptive,
title = {{Adaptive confidence intervals with missing data}},
author = {Tianyi Ma and Kabir A. Verchand and Chao Gao and Richard J. Samworth},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28336},
eprint = {2609.28336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28336},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Adaptive confidence intervals with missing data
AU - Tianyi Ma
AU - Kabir A. Verchand
AU - Chao Gao
AU - Richard J. Samworth
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28336
UR - https://arxiv.org/abs/2609.28336
AB - We consider the construction of confidence intervals for population means when observations are subject to missingness. To accommodate more general missingness mechanisms than missing completely at random (MCAR), we adopt a reparametrised version of the realisable contamination model of Ma et al. (2026), which is a mixture of an MCAR version and a missing not at random version of the same base distribution P. We characterise the minimax length of confidence intervals that can adapt to potentially unknown parameters of the model, including the contamination fraction, for Gaussian base distributions and for nonparametric classes satisfying certain tail or symmetry assumptions. In all of these settings, we provide explicit constructions of simple, practical and finite-sample valid adaptive confidence intervals that attain the corresponding minimax rates. Finally, we provide implications of our results for causal inference.
ER -