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

Frink, N.; Schmid, T.; Würz, N.

Abstract: The paper proposes a generalized mixed effects random forest framework for small area estimation under generalized modelling assumptions. The approach combines machine learning techniques for identifying nonlinear relationships with random effects that account for hierarchical structures in the data. It accommodates response variables from the exponential family through general link functions and develops a parametric bootstrap for mean squared error estimation. Simulation studies assess both point and uncertainty estimation and investigate the effects of converting continuous outcomes into binary variables. The methodology is applied to estimate poverty rates and reveal spatial patterns of poverty in the Mexican state of Tlaxcala.

Nicolas Frink, Timo Schmid & Nora Würz (2026): Small area estimation with generalized random forests: estimating poverty rates in Mexico, Journal of the Royal Statistical Society Series A: Statistics in Society, forthcoming, DOI: https://doi.org/10.1093/jrsssa/qnag092

Krennmair, P.; Würz, N.; Schmid, T.; Tzavidis, N.

Abstract: The paper studies random forest and mixed effects random forest methods for the estimation of general small area parameters. To account for between-area heterogeneity, the proposed mixed effects random forest incorporates area-specific random effects and uses a new fitting algorithm with bootstrap bias correction for the random forest residual variance. General small area parameters are estimated through an area-specific distribution function, while uncertainty is assessed using a nonparametric block bootstrap. The methodology is applied to household consumption data from Mozambique to estimate district-level poverty indicators, including the head count ratio and poverty gap. Comparisons with model-based and direct estimators illustrate the benefits of incorporating random effects, the relevance of suitable data transformations, and the robustness of random forest-type methods. The results also emphasize that machine learning methods for small area estimation require careful statistical modelling rather than a purely black-box application.

Patrick Krennmair, Nora Würz, Timo Schmid & Nikos Tzavidis (2026): Random forests and mixed effects random forests for small area estimation of general parameters: A poverty mapping case study in Mozambique, The Annals of Applied Statistics, 20(1), 809–832. DOI: https://doi.org/10.1214/25-AOAS2126 

We are pleased to welcome Johanna Einhorn to the Chair of Statistics and Econometrics.

Frink, N.; Schmid, T. 

Abstract: Small area estimation methods are proposed that use generalized tree-based machine learning techniques to improve the estimation of disaggregated means in small areas using discrete survey data. Specifically, two existing approaches based on random forests - the Generalized Mixed Effects Random Forest (GMERF) and a Mixed Effects Random Forest (MERF) - are extended to accommodate count outcomes, addressing key challenges such as overdispersion. Additionally, three bootstrap methodologies designed to assess the reliability of point estimators for area-level means are evaluated. The numerical analysis shows that the MERF, which does not assume a Poisson distribution to model the mean behavior of count data, excels in scenarios of severe overdispersion. Conversely, the GMERF performs best under conditions where Poisson distribution assumptions are moderately met. In a case study using real-world data from the state of Guerrero, Mexico, the proposed methods effectively estimate area-level means while capturing the uncertainty inherent in overdispersed count data. These findings highlight their practical applicability for small area estimation.

Nicolas Frink & Timo Schmid (2025) Small area prediction of counts under machine learning-type mixed models, Computational Statistics & Data Analysis, DOI: https://doi.org/10.1016/j.csda.2025.108218