Small area learning
Abstract
Small area estimation (SAE) traditionally borrows strength across domains through a prespecified working model. We introduce small area learning (SAL), a learner-agnostic framework that formulates SAE as a multi-target semi-supervised learning problem and treats outcome prediction as a nuisance task. Areas may differ through unrestricted covariate shift and structured conditional shift, with information shared through common and area-specific components. We develop standard and cross-fitted estimators for low-complexity and flexible learners, unifying synthetic, model-based, and fully residual-corrected estimation. For area means, we establish consistency and asymptotic normality and provide variance estimators and confidence intervals. We extend the theory to settings with only aggregated population covariates and characterize the resulting aggregation bias. SAL reveals a bias--variance trade-off: partial residual correction can reduce mean squared error, whereas full correction yields estimators robust to working-model misspecification, potentially at higher variance. Simulations yield RMSE reductions of 34\%--49\% relative to direct estimation, with the best configuration varying across settings. An empirical application favours a cross-fitted estimator using a flexible learner under the chosen validation criterion. The numerical studies also illustrate how shrinkage can produce overly optimistic confidence intervals at the expense of strong modeling assumptions.
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BibTeX
@misc{reluga2026small,
title = {{Small area learning}},
author = {Katarzyna Reluga and Nicola Salvati and Setareh Ranjbar and Nikos Tzavidis and Mark van der Laan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15953},
eprint = {2610.15953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15953},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Small area learning
AU - Katarzyna Reluga
AU - Nicola Salvati
AU - Setareh Ranjbar
AU - Nikos Tzavidis
AU - Mark van der Laan
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15953
UR - https://arxiv.org/abs/2610.15953
AB - Small area estimation (SAE) traditionally borrows strength across domains through a prespecified working model. We introduce small area learning (SAL), a learner-agnostic framework that formulates SAE as a multi-target semi-supervised learning problem and treats outcome prediction as a nuisance task. Areas may differ through unrestricted covariate shift and structured conditional shift, with information shared through common and area-specific components. We develop standard and cross-fitted estimators for low-complexity and flexible learners, unifying synthetic, model-based, and fully residual-corrected estimation. For area means, we establish consistency and asymptotic normality and provide variance estimators and confidence intervals. We extend the theory to settings with only aggregated population covariates and characterize the resulting aggregation bias. SAL reveals a bias--variance trade-off: partial residual correction can reduce mean squared error, whereas full correction yields estimators robust to working-model misspecification, potentially at higher variance. Simulations yield RMSE reductions of 34\%--49\% relative to direct estimation, with the best configuration varying across settings. An empirical application favours a cross-fitted estimator using a flexible learner under the chosen validation criterion. The numerical studies also illustrate how shrinkage can produce overly optimistic confidence intervals at the expense of strong modeling assumptions.
ER -