Bayesian Small Area Estimation of Proportions Using Archimedean Copula Models with Random Effects

Music City Center 

This study addresses the challenge of estimating proportions for small areas, particularly when sample sizes are small or even zero, leading to unreliable direct estimates. We propose a Bayesian approach using a new probability model class that incorporates random effects to account for variations between small areas. These models are based on exchangeable Archimedean copulas, allowing for flexible extra binomial variation modeling. The Bayesian inference involves obtaining the posterior distribution of the random effect and its Laplace transform, which is then used to derive Bayes estimates of small area proportions. Model parameters are estimated using maximum likelihood, and the Akaike information criterion (AIC) is used for model selection. We also develop empirical best predictors (EBP) and empirical best linear unbiased predictors (EBLUP) for small area proportions and propose a jackknife method to estimate the prediction mean squared error (PMSE) of these predictors. The methods are illustrated through simulated and real data examples, demonstrating their effectiveness in providing reliable small-area estimates. This work contributes to the growing literature on small-area e

Small Area Estimation

Bayesian Inference

Archimedean Copulas, Random Effects

Empirical Best Predictor (EBP)

Maximum Likelihood Estimation

Jackknife Method 

Section on Bayesian Statistical Science