Robust Small Area Estimation under Spatial Non‐stationarity

The effective use of spatial information in a regression‐based approach to small area estimation is an important practical issue. One approach to account for geographic information is by extending the linear mixed model to allow for spatially correlated random area effects. An alternative is to include the spatial information by a non‐parametric mixed models. Another option is geographic weighted regression where the model coefficients vary spatially across the geography of interest. Although these approaches are useful for estimating small area means efficiently under strict parametric assumptions, they can be sensitive to outliers. In this paper, we propose robust extensions of the geographically weighted empirical best linear unbiased predictor. In particular, we introduce robust projective and predictive estimators under spatial non‐stationarity. Mean squared error estimation is performed by two analytic approaches that account for the spatial structure in the data. Model‐based simulations show that the methodology proposed often leads to more efficient estimators. Furthermore, the analytic mean squared error estimators introduced have appealing properties in terms of stability and bias. Finally, we demonstrate in the application that the new methodology is a good choice for producing estimates for average rent prices of apartments in urban planning areas in Berlin.