Divide and Conquer strategy for Multivariate Fay-Herriot models.

A. Aneiros-Batista, M. J. Lombardía Cortiña, E. López-Vizcaíno, S. A. Sperlich

Area-level models are central to small area estimation (SAE), but computational demands grow with dataset size. We introduce a Divide and Conquer framework for multivariate Fay–Herriot models that decomposes the estimation into smaller, independent sub-systems, integrating results via a principled aggregation step. This method preserves the full model's statistical properties while reducing computational costs and improving stability in high-dimensional or ill-conditioned settings.

Simulations with bi-, tri-, and tetravariate populations confirm that this approach yields nearly unbiased estimates comparable to the global estimator, but with faster execution. The methodology is applied to the 2024 Spanish Quarterly Labour Cost Survey, providing efficient SAE predictions of mean wage costs and hours by sector and firm size. This strategy offers a scalable framework for modern applications where dimensionality and heterogeneity make traditional joint estimation impractical.

Keywords: Computational efficiency, Divide and Conquer, Multivariate Fay–Herriot models, Labour cost survey

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September 4, 2026  11:10 AM
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