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

TL;DR

This paper introduces a Bayesian spectral clustering model for Small Area Estimation that incorporates external covariates, providing flexible benchmarking and uncertainty quantification, demonstrated through simulations and a Colombian internet access case study.

Contribution

It proposes a novel Bayesian spectral clustering approach for SAE, integrating external covariates and benchmarking with new uncertainty measures, advancing existing methodologies.

Findings

FH-SC outperforms traditional methods in simulations

The CPMSE effectively quantifies uncertainty in benchmarking

Case study shows practical advantages of FH-SC in real data

Abstract

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.