Comparative Study of MSE Estimates for Small Area Models Under Different Sampling Variances

• Activity Number: 474 - New Advances in Modeling Survey Data
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Survey Research Methods Section
• Author(s): Kyle Irimata* and Gauri Datta and Jerry Maples
• Companies: U.S. Census Bureau and U.S. Census Bureau/University of Georgia and U.S. Census Bureau
• Keywords: Small area estimation; Fay Herriot; Mean squared error

Abstract

The Fay-Herriot model is a popular linear mixed effects model for estimating small area means. Many approximations for the mean squared error (MSE) of the empirical best linear unbiased predictor of the small area means have been produced for this model. Amongst other things, these MSE approximations depend on the estimated sampling variance and estimates of the model parameters. However, estimation of the random effects variance can be difficult when the sampling variances are comparatively large and dispersed, which in turn can impact the estimation of the MSE. We compare the estimation of the random effects variance and the corresponding MSE estimates for various approaches such as those proposed by Prasad and Rao and by Fay and Herriot, under different sampling variance patterns and random effects distributions. For illustration, we use data from the American Community Survey and tax records to estimate childhood poverty in the U.S.