Pseudo-Bayesian Small Area Estimation

• Activity Number: 332 - Estimation and Survey
• Type: Contributed
• Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Government Statistics Section
• Author(s): Gauri Sankar Datta* and Juhyung Lee and Jiacheng Li
• Companies: US Census Bureau/University of Georgia and University of Florida and University of Georgia
• Keywords: Empirical best linear unbiased prediction; Fay-Herriot model; Model misspecification; Observed best prediction; Robustness

Abstract

The main goal in small area estimation is estimation of means of small areas. The observed best prediction (OBP) is a model-based prediction procedure for small area means that is proposed as an alternative to the empirical best linear unbiased prediction (EBLUP). The OBP method proposes an objective function to estimate the model parameters. We use this objective function to construct a pseudo likelihood for the model parameters. Using this we propose pseudo-Bayesian estimates of small area means for the Fay-Herriot model. Also, the PBE credible intervals attain the nominal coverage probability, while the OBP confidence intervals exhibit unsatisfactory coverage. Our simulations to investigate the robustness of the various predictors to mean misspecification show that the PBE predictors retain all the robustness enjoyed by the EBLUP and the OBP predictors. Simulations and data analysis show that the PBE predictors enjoy competitive frequentist properties over OBP and the EBLUPs. Being Bayesian by construction, the proposed PBE predictors admit a dual justification as optimal predictors, and they are expected to be attractive to practitioners.