Regularized Small Area Estimation with Graph Laplacian Benchmarking priors
Abstract
Small area estimation (SAE) often requires both borrowing information across areas and benchmarking estimates to reliable aggregates. We develop a Bayesian framework that addresses these two objectives jointly through a new family of Benchmarking priors. The priors are induced by a benchmark-constrained regularization problem. The resulting family includes a Benchmarking Prior that incorporates the benchmarking restrictions without additional regularization across areas, and Single and Multi-View Laplacian Benchmarking Priors that introduce regularization through graph Laplacians constructed from area similarities based on external covariate information. For posterior computation under these degenerate priors, we develop tailored MCMC algorithms based on a reduced parameterization of the constraint space. We assess the proposed models using a data-based simulation and apply the framework to estimate Average Household Size (AHS) at the municipality level in Colombia in 2025. In this application, graph-based regularization improves model performance, with the Multi-View models generally producing more precise municipality-level estimates.
Related
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BibTeX
@misc{fuquenepatino2026regularized,
title = {{Regularized Small Area Estimation with Graph Laplacian Benchmarking priors}},
author = {Jairo Fúquene-Patiño and Brenda Betancourt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11266},
eprint = {2610.11266},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11266},
}
RIS
TY - UNPB
TI - Regularized Small Area Estimation with Graph Laplacian Benchmarking priors
AU - Jairo Fúquene-Patiño
AU - Brenda Betancourt
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11266
UR - https://arxiv.org/abs/2610.11266
AB - Small area estimation (SAE) often requires both borrowing information across areas and benchmarking estimates to reliable aggregates. We develop a Bayesian framework that addresses these two objectives jointly through a new family of Benchmarking priors. The priors are induced by a benchmark-constrained regularization problem. The resulting family includes a Benchmarking Prior that incorporates the benchmarking restrictions without additional regularization across areas, and Single and Multi-View Laplacian Benchmarking Priors that introduce regularization through graph Laplacians constructed from area similarities based on external covariate information. For posterior computation under these degenerate priors, we develop tailored MCMC algorithms based on a reduced parameterization of the constraint space. We assess the proposed models using a data-based simulation and apply the framework to estimate Average Household Size (AHS) at the municipality level in Colombia in 2025. In this application, graph-based regularization improves model performance, with the Multi-View models generally producing more precise municipality-level estimates.
ER -