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Abstract:
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Many private, governmental, and academic researchers require the inferential tools of small area estimation. Such models are designed to “borrow strength” from similar units in the absence of sufficient data for direct estimation. The well-known Fay-Herriot model is one such approach, and it has been a popular choice for application and modification. In particular, its parametric assumptions and their potential shortcomings have motivated alternative models more robust to outliers and misspecification. We continue this work, and instead of trading one set of parametric assumptions for another (e.g. normality for heavy-tailed errors), we augment the typical Fay-Herriot likelihood with a non-parametric correction term. This agnostic Fay-Herriot (AFH) model retains many of the desirable qualities of the original Fay-Herriot model without requiring strict normality. We compare the AFH model to empirical Bayes and frequentist estimators of the original Fay-Herriot model on a range of simulated and real-world data.
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