Spatially Robust Inference with Predicted and Missing at Random Labels

• URL: http://arxiv.org/abs/2603.11368v1
• Date: Wed, 11 Mar 2026 23:14:21 GMT
• Title: Spatially Robust Inference with Predicted and Missing at Random Labels
• Abstract summary: We show that cross-fitting induces fold-level correlation that distorts spatial variance estimators, producing unstable or overly conservative confidence intervals.<n>We also propose a jackknife spatial heterosasticity and auto consistent (HAC) variance correction that separates dependence from fold-induced noise.
• Score: 2.5574009994099196
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: When outcome data are expensive or onerous to collect, scientists increasingly substitute predictions from machine learning and AI models for unlabeled cases, a process which has consequences for downstream statistical inference. While recent methods provide valid uncertainty quantification under independent sampling, real-world applications involve missing at random (MAR) labeling and spatial dependence. For inference in this setting, we propose a doubly robust estimator with cross-fit nuisances. We show that cross-fitting induces fold-level correlation that distorts spatial variance estimators, producing unstable or overly conservative confidence intervals. To address this, we propose a jackknife spatial heteroscedasticity and autocorrelation consistent (HAC) variance correction that separates spatial dependence from fold-induced noise. Under standard identification and dependence conditions, the resulting intervals are asymptotically valid. Simulations and benchmark datasets show substantial improvement in finite-sample calibration, particularly under MAR labeling and clustered sampling.

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