Abstract:
When sample sizes are too small to produce reliable direct estimates in survey statistics, the model-based methods are often used to obtain population-level quantities of interest for those small geographical areas or small population subgroup domains. One well-known model for small area/domain level estimates is the Fay-Herriot model, which can be interpreted as a linear mixed effects model in which the true domain-level means are normally distributed. However, it is challenging to verify their distributional assumption since they are not directly observable. In this paper, we formulate a semi-parametric extension of the Fay-Herriot model in which the default normality assumption for the true means is replaced by a nonparametric specification. While we investigate the intercept-only model, which is often used in the absence of the domain-level covariates, we illustrate the robustness of our estimators for domain-level means as well as the distribution of their “ensemble” through simulations under different distributional assumptions. Viability of the approach and the effects are illustrated using the 2008 National Survey of Recent College Graduates to estimate mean salaries for demographic subgroups of interest.
Keywords:
Complex survey, Dirichlet process prior, Fay-Herriot model, National Survey of Recent College Graduates, Small area estimation
tr195.pdf