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Abstract We develop a Bayesian model–based approach to finite population estimation accounting for spatial dependence. Our innovation here is a framework that achieves inference for finite population quantities in spatial process settings. A key distinction from the small area estimation setting is that we analyze finite populations referenced by their geographic coordinates. Specifically, we consider a two‐stage sampling design in which the primary units are geographic regions, the secondary units are point‐referenced locations, and the measured values are assumed to be a partial realization of a spatial process. Estimation of finite population quantities from geostatistical models does not account for sampling designs, which can impair inferential performance, whereas design‐based estimates ignore the spatial dependence in the finite population. We demonstrate by using simulation experiments that process‐based finite population sampling models improve model fit and inference over models that fail to account for spatial correlation. Furthermore, the process‐based models offer richer inference with spatially interpolated maps over the entire region. We reinforce these improvements and demonstrate scalable inference for groundwater nitrate levels in the population of California Central Valley wells by offering estimates of mean nitrate levels and their spatially interpolated maps.
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Spatially selected and dependent random effects for small area estimation with application to rent burden
Abstract Area-level models for small area estimation typically rely on areal random effects to shrink design-based direct estimates towards a model-based predictor. Incorporating the spatial dependence of the random effects into these models can further improve the estimates when there are not enough covariates to fully account for the spatial dependence of the areal means. A number of recent works have investigated models that include random effects for only a subset of areas, in order to improve the precision of estimates. However, such models do not readily handle spatial dependence. In this paper, we introduce a model that accounts for spatial dependence in both the random effects as well as the latent process that selects the effects. We show how this model can significantly improve predictive accuracy via an empirical simulation study based on data from the American Community Survey, and illustrate its properties via an application to estimate county-level median rent burden.
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- Award ID(s):
- 2215169
- PAR ID:
- 10610392
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series A: Statistics in Society
- ISSN:
- 0964-1998
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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