Abstract:
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One of the main interests in small area estimation (SAE) is prediction of the small area means. Under the widely used Fay-Herriot (FH) model in SAE, this is equivalent to prediction of the mixed effects, each of which is composed of the mean function and the area-specific random effect. In general, the mean function is a linear combination of known covariates and unknown regression coefficients. When an important covariate is not used in the model, the FH model will lead to a poor prediction of the small area means. We propose a remedial modification of the FH model in such situation by introducing an extra random effect term to the model to capture exchangeability of the random small area effects. For time series data, we show that the modified model can help recover the dependence structure among the small area means and hence achieves an improved prediction when an important covariate is omitted. We illustrate our findings using household income data from the Current Population Survey collected over a nine-year period from the U.S. Census Bureau.
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