Blockwise Missingness meets AI: A Tractable Solution for Semiparametric Inference

• URL: http://arxiv.org/abs/2509.24158v1
• Date: Mon, 29 Sep 2025 01:17:28 GMT
• Title: Blockwise Missingness meets AI: A Tractable Solution for Semiparametric Inference
• Authors: Qi Xu, Lorenzo Testa, Jing Lei, Kathryn Roeder,
• Abstract summary: We consider parameter estimation and inference when data feature blockwise, non-monotone missingness.<n>Our approach, rooted in semiparametric theory and inspired by prediction-powered inference, leverages off-the-shelf AI (predictive or generative) models to handle missing completely at random mechanisms.
• Score: 22.72439408201187
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider parameter estimation and inference when data feature blockwise, non-monotone missingness. Our approach, rooted in semiparametric theory and inspired by prediction-powered inference, leverages off-the-shelf AI (predictive or generative) models to handle missing completely at random mechanisms, by finding an approximation of the optimal estimating equation through a novel and tractable Restricted Anova hierarchY (RAY) approximation. The resulting Inference for Blockwise Missingness(RAY), or IBM(RAY) estimator incorporates pre-trained AI models and carefully controls asymptotic variance by tuning model-specific hyperparameters. We then extend IBM(RAY) to a general class of estimators. We find the most efficient estimator in this class, which we call IBM(Adaptive), by solving a constrained quadratic programming problem. All IBM estimators are unbiased, and, crucially, asymptotically achieving guaranteed efficiency gains over a naive complete-case estimator, regardless of the predictive accuracy of the AI models used. We demonstrate the finite-sample performance and numerical stability of our method through simulation studies and an application to surface protein abundance estimation.

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