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Small area estimation has become an important tool in official statistics,used to construct estimates of population quantities for domains with smallsample sizes. Typical area-level models function as a type of heteroscedasticregression, where the variance for each domain is assumed to be known andplugged in following a design-based estimate. Recent work has consideredhierarchical models for the variance, where the design-based estimates are usedas an additional data point to model the latent true variance in each domain.These hierarchical models may incorporate covariate information, but can bedifficult to sample from in high-dimensional settings. Utilizing recentdistribution theory, we explore a class of Bayesian hierarchical models forsmall area estimation that smooth both the design-based estimate of the meanand the variance. In addition, we develop a class of unit-level models forheteroscedastic Gaussian response data. Importantly, we incorporate bothcovariate information as well as spatial dependence, while retaining aconjugate model structure that allows for efficient sampling. We illustrate ourmethodology through an empirical simulation study as well as an applicationusing data from the American Community Survey.

Conjugate Modeling Approaches for Small Area Estimation with Heteroscedastic Structure