Global-local shrinkage priors for modeling random effects in multivariate spatial small area estimation

TL;DR

This paper introduces a Bayesian multivariate spatial small area estimation model with global-local shrinkage priors, enhancing flexibility, robustness, and spatial correlation modeling for improved estimation accuracy.

Contribution

It develops a novel Bayesian framework with component-specific shrinkage and spatial dependence, advancing multivariate small area estimation methods.

Findings

Improved estimation accuracy in simulations.

Effective modeling of spatial dependence.

Robustness against excessive shrinkage.

Abstract

Small area estimation (SAE) plays a central role in survey statistics and epidemiology, providing reliable estimates for domains with limited sample sizes. The multivariate Fay-Herriot model has been extensively used for this purpose, because it enhances estimation accuracy by borrowing strength across multiple correlated variables. In this paper, we develop a Bayesian extension of the multivariate Fay-Herriot model that enables flexible, component-specific shrinkage of the random effects. The proposed approach employs global-local priors formulated through a sandwich mixture representation, allowing adaptive regularization of each element of the random-effect vectors. This construction yields greater robustness and prevents excessive shrinkage in areas exhibiting strong underlying signals. In addition, we incorporate spatial dependence into the model to account for geographical correlation across small areas. The resulting spatial multivariate framework simultaneously exploits cross-variable relationships and spatial structure, yielding improved estimation efficiency. The utility of the proposed method is demonstrated through simulation studies and an empirical application to real survey data.