New Approaches for Handling Nonlinearity in Area-level Small Area Estimation

Thomas M. Menino Convention & Exhibition Center 

Small area estimation models are critical for dissemination and understanding of important population characteristics within sub-domains that often have limited sample size. The classic Fay-Herriot model is perhaps the most widely used approach to generate such estimates. However, a limiting assumption of this approach is that the latent true population quantity has a linear relationship with the given covariates. We introduce two new approaches that allow for estimation of nonlinear relationships between the true population quantity and the covariates. First, through the use of random weight neural networks, we develop a Bayesian hierarchical extension of the Fay-Herriot model. Second, we consider the use of Bayesian additive regression trees (BART) embedded within a Fay-Herriot model. We illustrate our approaches through an empirical simulation study as well as an analysis of median household income for census tracts in the state of California.