Nonlinear Fay-Herriot Models for Small Area Estimation Using Random Weight Neural Networks

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. Through the use of random weight neural networks, we develop a Bayesian hierarchical extension of this framework that allows for estimation of nonlinear relationships between the true population quantity and the covariates. We illustrate our approach through an empirical simulation study as well as an analysis of median household income for census tracts in the state of California.