Abstract

Existing methods for handling nonignorable missing data often rely

on strong modeling assumptions, making them vulnerable to model misspecification. This paper proposes a conformal prediction framework for constructing

prediction sets under nonignorable missing responses, which is model-free for the

outcome regression while relying on a consistently estimated propensity score.

Our framework addresses two central challenges posed by nonignorable missingness: non-identifiability and the lack of data exchangeability. The key idea is to

construct the highest conditional density prediction set using a local subset near

the target point, while correcting for selection bias via modeling the missingness

mechanism. Within this framework, we develop a bias-adjusted semiparametric

method for conditional density estimation, which fits a quantile process to the

observed data and corrects for bias using propensity weights.

This estimator

integrates seamlessly into the conformal framework, allowing our approach to

guarantee not only marginal coverage, but also local and asymptotic conditional

coverage for any new subject, while achieving asymptotically optimal interval

lengths. We demonstrate the validity and efficiency of our procedure through

simulation studies and an application to a real HIV-CD4 dataset.

Information

Preprint No.SS-2025-0156
Manuscript IDSS-2025-0156
Complete AuthorsMenghan Yi, Yingying Zhang, Yanlin Tang, Huixia Judy Wang
Corresponding AuthorsYanlin Tang
Emailsyanlintang2018@163.com

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Acknowledgments

We sincerely thank the Editor, Associate Editor, and two anonymous reviewers for their constructive comments and helpful suggestions. The re-

search of Tang and Zhang was partially supported by the National Natural Science Foundation of China (grants 12371265 and 12471280), Funda-

mental and Interdisciplinary Disciplines Breakthrough Plan of the Ministry

of Education of China (grant JYB2025XDXM904) and Chern Institute of

Mathematics, Nankai University, and the research of Wang was partially

supported by the National Science Foundation (grant DMS-2436216).

Supplementary Materials

The online Supplementary Materials provided detailed technical proofs,

high-dimensional extensions, and additional numerical experiments.

Supplementary materials are available for download.