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Abstract:
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The Fay-Herriot model is a popular approach for estimating small area means using a linear mixed effects model. It links the means through a multiple linear regression on a set of covariates. In various applications some of the model assumptions may fail to hold, such as a lack of normality of the model errors. In small samples with few small areas, estimation of the model parameters and the mean squared error (MSE) may also pose a challenge. In this work, we generalize the standard Fay-Herriot model by allowing the model error terms to be non-normal. We introduce a set of estimators of the model parameters using estimating equations, as well as corresponding analytic expressions of the MSE. In addition, we propose a nonparametric bootstrapping method for estimating MSE using a distribution that matches the moments of the data. We provide the results of a simulation study and compare the proposed analytic and bootstrap-based estimators of MSE with existing approaches. We apply these approaches to county-level poverty counts in Maryland and Georgia.
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