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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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Robust Small Area Estimation: An Overview
A small area typically refers to a subpopulation or domain of interest for which a reliable direct estimate, based only on the domain-specific sample, cannot be produced due to small sample size in the domain. While traditional small area methods and models are widely used nowadays, there have also been much work and interest in robust statistical inference for small area estimation (SAE). We survey this work and provide a comprehensive review here.We begin with a brief review of the traditional SAE methods. We then discuss SAEmethods that are developed under weaker assumptions and SAE methods that are robust in certain ways, such as in terms of outliers or model failure. Our discussion also includes topics such as nonparametric SAE methods, Bayesian approaches, model selection and diagnostics, and missing data. A brief review of software packages available for implementing robust SAE methods is also given.
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- Award ID(s):
- 1915976
- PAR ID:
- 10170761
- Date Published:
- Journal Name:
- Annual review of statistics and its application
- Volume:
- 7
- ISSN:
- 2326-8298
- Page Range / eLocation ID:
- 337-360
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1146/annurev-statistics-031219-041212
