arXiv subjects

Jairo Fúquene-Patiño

Publications and source records attributed to Jairo Fúquene-Patiño.

3 recordsLinked to original sources

arXiv2026

Fully Bayesian Spectral Clustering and Benchmarking with Uncertainty Quantification for Small Area Estimation

In this work, inspired by machine learning techniques, we propose a new Bayesian model for Small Area Estimation (SAE), the Fay-Herriot model with Spectral Clustering (FH-SC). Unlike traditional approaches, clustering in FH-SC is based on spectral clustering algorithms that utilize external covariates, rather than geographical or administrative criteria. A major advantage of the FH-SC model is its flexibility in integrating existing SAE approaches, with or without clustering random effects. To enable benchmarking, we leverage the theoretical framework of posterior projections for constrained Bayesian inference and derive closed form expressions for the new Rao-Blackwell (RB) estimators of the posterior mean under the FH-SC model. Additionally, we introduce a novel measure of uncertainty for the benchmarked estimator, the Conditional Posterior Mean Square Error (CPMSE), which is generalizable to other Bayesian SAE estimators. We conduct model-based and data-based simulation studies to evaluate the frequentist properties of the CPMSE. The proposed methodology is motivated by a real case study involving the estimation of the proportion of households with internet access in the municipalities of Colombia. Finally, we also illustrate the advantages of FH-SC over existing Bayesian and frequentist approaches through our case study.

stat.ME↗

arXiv2026

Regularized Small Area Estimation with Graph Laplacian Benchmarking priors

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.

stat.ME↗

arXiv2026

On improving the estimates of the sampling variances via Global-Local priors in Small Area Estimation

The Fay-Herriot (FH) model is widely used in official statistics to produce reliable estimates for domains with small sample sizes. In the classical FH model, the sampling variances are treated as known, even though they are typically estimated from the data. In practice, these variance estimates can be highly variable. To address this issue, practitioners often use Generalized Variance Functions (GVFs) to borrow strength across areas and stabilize estimation. In this work, we propose a new Bayesian model to improve the posterior estimation of the sampling variances in Small Area Estimation (SAE). Our proposed model incorporates Global-Local (GL) priors to improve the level of shrinkage toward the posterior estimates obtained with the GVF function. We study the theoretical properties of the proposed model and develop adaptive Markov chain Monte Carlo (MCMC) algorithms to address computational challenges arising from conditional distributions involving Gamma functions. The performance of the proposed Bayesian model is investigated through simulation studies and compared with competing approaches. Finally, we implement our proposal in two real applications by estimating the Corn production from the U.S. Department of Agriculture and the Prevalence of the Educational Attainment Index at the municipality levels in Colombia.

stat.ME↗