Abstract:
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In survey statistics, small area methods and models are used to produce estimates (for instance, average salaries) for geographical areas or population subgroups for which the sample is too small to support direct estimation. One well known model is the Fay-Herriot model, which can be interpreted as a linear mixed effects model in which normality for random effects is assumed. Because random effects are not observed, it is difficult to check the assumption of normality (or any other parametric assumption). In this presentation, we consider extensions of the Fay-Herriot model in which the default normality assumption for the random effects is replaced by a non-parametric specification. We explore the estimation of individual area means as well as the distribution of their ensemble. Viability of the approach and the effects are investigated using the National Survey of Recent College Graduates to estimate average salaries for different demographic subgroups.
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