Small area learning

원문 초록

Small area estimation (SAE) traditionally borrows strength across domains through a prespecified working model. We introduce small area learning (SAL), a novel 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 estimators with and without cross-fitting, accommodating low-complexity and flexible learners and unifying synthetic, model-based, and semi-supervised estimators. For area means, we establish a unified asymptotic theory for these estimator families, characterizing conditions for consistency, asymptotic normality and providing variance estimators and confidence intervals without prescribing a particular learning algorithm. We extend the theory to settings with only aggregated population covariates and characterize the resulting aggregation bias. SAL reveals clearly a bias-variance trade-off: partial residual correction in classical estimators can reduce mean squared error, whereas full correction yields estimators robust to the misspecification of working models, potentially at higher variance. Simulations yield RMSE reductions of 34%-49% relative to direct estimation, with the best configuration varying across settings. The numerical studies also illustrate how shrinkage can produce overly optimistic confidence intervals at the expense of strong modeling assumptions.