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.