Agnostic Model-Assisted Estimation with Machine Learning for Survey Data
Abstract
Model-assisted estimation uses prediction rules to improve the efficiency of estimators of finite population parameters while retaining design-based inference. Although flexible prediction methods have been considered, existing theoretical results are largely method-specific. We develop a learner-agnostic framework that replaces separate analyses for individual learners with general conditions on the sampling design and prediction error. We connect design-aware and design-agnostic cross-fitting and characterize the sampling designs under which they yield conditional independence across folds. Under suitable conditions, conditional weighting gives exact design-unbiasedness. We establish first-order equivalence to oracle estimators, leading to design consistency and asymptotic normality, and clarify when conditional and original inclusion probabilities yield the same first-order behavior. We propose consistent variance estimators based on cross-fitted residuals and construct asymptotically valid confidence intervals. Under additional model and regularity conditions, we establish asymptotic optimality through attainment of the Godambe--Joshi lower bound. Simulations show that cross-fitting substantially reduces finite-sample bias and improves variance estimation and coverage with adaptive learners.
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BibTeX
@misc{an2026agnostic,
title = {{Agnostic Model-Assisted Estimation with Machine Learning for Survey Data}},
author = {Ziming An and Mehdi Dagdoug and David Haziza and Yves Tillé},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10904},
eprint = {2609.10904},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10904},
}
RIS
TY - UNPB
TI - Agnostic Model-Assisted Estimation with Machine Learning for Survey Data
AU - Ziming An
AU - Mehdi Dagdoug
AU - David Haziza
AU - Yves Tillé
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10904
UR - https://arxiv.org/abs/2609.10904
AB - Model-assisted estimation uses prediction rules to improve the efficiency of estimators of finite population parameters while retaining design-based inference. Although flexible prediction methods have been considered, existing theoretical results are largely method-specific. We develop a learner-agnostic framework that replaces separate analyses for individual learners with general conditions on the sampling design and prediction error. We connect design-aware and design-agnostic cross-fitting and characterize the sampling designs under which they yield conditional independence across folds. Under suitable conditions, conditional weighting gives exact design-unbiasedness. We establish first-order equivalence to oracle estimators, leading to design consistency and asymptotic normality, and clarify when conditional and original inclusion probabilities yield the same first-order behavior. We propose consistent variance estimators based on cross-fitted residuals and construct asymptotically valid confidence intervals. Under additional model and regularity conditions, we establish asymptotic optimality through attainment of the Godambe--Joshi lower bound. Simulations show that cross-fitting substantially reduces finite-sample bias and improves variance estimation and coverage with adaptive learners.
ER -