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Gradient boosting for hierarchical data in small area estimation

Messer, P.; Schmid, T.

Abstract: The paper proposes a Mixed Effects Gradient Boosting (MEGB) approach for small area estimation that combines the flexibility of gradient boosting with random effects to account for hierarchical data structures. The method allows nonlinear relationships and interactions to be modelled while capturing unobserved heterogeneity across domains. Area-level means are obtained from unit-level predictions, and a nonparametric bootstrap is used for mean squared error estimation. The performance of MEGB is evaluated in model-based and design-based simulation studies and compared with established small area estimators. The results demonstrate the potential of the approach for flexible prediction in hierarchical small area settings.

Paul Messer & Timo Schmid (2026): Gradient boosting for hierarchical data in small area estimation, Statistics and Computing, 36, 218, DOI: https://doi.org/10.1007/s11222-026-10970-1