Conjugate Modeling Approaches for Small Area Estimation with Heteroscedastic Structure

TL;DR

This paper introduces conjugate Bayesian hierarchical models for small area estimation that jointly smooth mean and variance estimates, incorporating covariates and spatial dependence for improved accuracy and computational efficiency.

Contribution

It develops a class of conjugate hierarchical models for small area estimation that handle heteroscedasticity, covariates, and spatial dependence efficiently.

Findings

Models perform well in empirical simulations

Application to American Community Survey data demonstrates practical utility

Efficient sampling enabled by conjugate model structure

Abstract

Small area estimation has become an important tool in official statistics, used to construct estimates of population quantities for domains with small sample sizes. Typical area-level models function as a type of heteroscedastic regression, where the variance for each domain is assumed to be known and plugged in following a design-based estimate. Recent work has considered hierarchical models for the variance, where the design-based estimates are used as an additional data point to model the latent true variance in each domain. These hierarchical models may incorporate covariate information, but can be difficult to sample from in high-dimensional settings. Utilizing recent distribution theory, we explore a class of Bayesian hierarchical models for small area estimation that smooth both the design-based estimate of the mean and the variance. In addition, we develop a class of unit-level models for heteroscedastic Gaussian response data. Importantly, we incorporate both covariate information as well as spatial dependence, while retaining a conjugate model structure that allows for efficient sampling. We illustrate our methodology through an empirical simulation study as well as an application using data from the American Community Survey.