Small Area Estimation with Linked Data

Abstract: In Small Area Estimation data linkage can be used to combine values of the variableof interest from a national survey with values of auxiliary variables obtained from another source like a population register. Linkage errors can induce bias when fitting regression models; moreover, they can create non-representative outliers in the linked data in addition to the presence of potential representative outliers. In this paper we adopt a secondary analyst's point view, assuming limited information is available on the linkage process, and we develop small area estimators based on linear mixed and linear M-quantile models to accommodate linked data containing a mix of both types of outliers. We illustrate the properties of these small area estimators, as well as estimators of their mean squared error, by means of model-based and design-based simulation experiments. These experiments show that the proposed predictors can lead to more efficient estimators when there is linkage error. Furthermore, the proposed mean-squared error estimation methods appear to perform well.