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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.
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Noniterative adjustment to regression estimators with population‐based auxiliary information for semiparametric models
Abstract Disease registries, surveillance data, and other datasets with extremely large sample sizes become increasingly available in providing population‐based information on disease incidence, survival probability, or other important public health characteristics. Such information can be leveraged in studies that collect detailed measurements but with smaller sample sizes. In contrast to recent proposals that formulate additional information as constraints in optimization problems, we develop a general framework to construct simple estimators that update the usual regression estimators with some functionals of data that incorporate the additional information. We consider general settings that incorporate nuisance parameters in the auxiliary information, non‐i.i.d. data such as those from case‐control studies, and semiparametric models with infinite‐dimensional parameters common in survival analysis. Details of several important data and sampling settings are provided with numerical examples.
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- Award ID(s):
- 1711952
- PAR ID:
- 10364218
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 79
- Issue:
- 1
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 140-150
- Size(s):
- p. 140-150
- Sponsoring Org:
- National Science Foundation
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