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Abstract Unit-level modeling strategies offer many advantages relative to the area-level models that are most often used in the context of small area estimation. For example, unit-level models aggregate naturally, allowing for estimates at any desired resolution, and also offer greater precision in many cases. We compare a variety of the methods available in the literature related to unit-level modeling for small area estimation. Specifically, to provide insight into the differences between methods, we conduct a simulation study that compares several of the general approaches. In addition, the methods used for simulation are further illustrated through an application to the American Community Survey. 

Abstract Model-based small area estimation is frequently used in conjunction with survey data to establish estimates for under-sampled or unsampled geographies. These models can be specified at either the area-level, or the unit-level, but unit-level models often offer potential advantages such as more precise estimates and easy spatial aggregation. Nevertheless, relative to area-level models, literature on unit-level models is less prevalent. In modeling small areas at the unit level, challenges often arise as a consequence of the informative sampling mechanism used to collect the survey data. This article provides a comprehensive methodological review for unit-level models under informative sampling, with an emphasis on Bayesian approaches. 

Abstract Small area estimation (SAE) 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 SAE 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.