# Spatially Robust Inference with Predicted and Missing at Random Labels

arXiv: https://arxiv.org/abs/2603.11368 · HTML: https://mlsanity.com/paper/2603.11368/

## Key facts

- Cited by 1 papers in the map (data through 7 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [A Unified Framework for Semiparametrically Efficient Semi-Supervised Learning](https://mlsanity.com/paper/2502.17741/) (2025)
- [From Narratives to Numbers: Valid Inference Using Language Model Predictions from Verbal Autopsy Narratives](https://mlsanity.com/paper/2404.02438/) (2024)
- [Another look at statistical inference with machine learning-imputed data](https://mlsanity.com/paper/2411.19908/) (2024)
- [Tailored inference for finite populations: conditional validity and transfer across distributions](https://mlsanity.com/paper/2104.04565/) (2021)
- [A Unified Framework for Inference with General Missingness Patterns and Machine Learning Imputation](https://mlsanity.com/paper/2508.15162/) (2025)
- [Consistency of common spatial estimators under spatial confounding](https://mlsanity.com/paper/2308.12181/) (2023)
- [General Covariance-Based Conditions for Central Limit Theorems with Dependent Triangular Arrays](https://mlsanity.com/paper/2308.12506/) (2023)
- [Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Data](https://mlsanity.com/paper/2512.05456/) (2025)

## Built on by (most cited first, 1 of 1)

- [Cluster-Robust Prediction-Powered Inference](https://mlsanity.com/paper/2610.09601/) (2026)

## Abstract (arXiv)

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.