Model-Based Screening for Robust Estimation in the Presence of Deviations from Linearity in Small Domain Models

Abstract Small domain estimation models, like the Fay-Herriot (FH), often assume a normally distributed latent process centered on a linear mean function. The linearity assumption may be violated for domains that express idiosyncratic phenomena not captured by the predictors. The direct sample estimate for such domain will be viewed as an outlier by FH when, in fact, it reflects an underlying true value. The model interpretation is also confounded by the variances of direct sample estimates because, while typically treated as fixed and known, they are estimates and thus contain noise. In this article, we construct a joint model for the direct estimates and their variances with nonparametric mixtures of normal distributions with the goal to improve robustness in estimation quality for these idiosyncratic domains. We devise a model-based screening tool to nominate domains where the model may not accurately account for deviations from the linearity assumption. We replace the modeled values for nominated domains with the direct estimate which we show robustify our models. The US Bureau of Labor Statistics’ Current Employment Statistics (CES) survey publishes monthly employment estimates for domains defined by industry and geography. Model estimation is performed for smaller domains to improve the reliability of the direct estimator. We compare fit performances for our candidate models under data constructed to be similar to the CES and conduct a simulation study to assess the robustness of our candidate models in the presence of deviations from linearity. We apply our model-based screening method and quantify its ability to improve the quality of published estimates.