A Spatially Nonstationary Fay-Herriot Model for Small Area Estimation

Small area estimates based on the widely-used area-level model proposed in Fay and Herriot (1979) assume that the area level direct estimates are spatially uncorrelated. In many cases, however, this is not the case. Extensions of the Fay-Herriot model to allow for spatial correlation have been proposed, but all assume spatial stationarity, i.e. the parameters of the associated regression model for the small area characteristic of interest do not vary spatially. Instead, spatial effects are introduced by imposing a spatial correlation structure on the regression errors. In this paper we propose an extension to the Fay-Herriot model that accounts for the presence of spatial nonstationarity, i.e. where the parameters of this regression model vary spatially. We refer to the predictor based on this extended model as the nonstationary empirical best linear unbiased predictor (NSEBLUP). We also develop two different estimators for the mean squared error of the NSEBLUP. The first estimator uses approximations similar to those in Opsomer et al. (2008). The second estimator is based on the parametric bootstrapping approach of Gonzalez-Manteiga et al. (2008) and Molina et al. (2009). Results from model-based and design-based simulation studies using spatially nonstationary data indicate that the NSEBLUP compares favourably with alternative area-level predictors that ignore this spatial nonstationarity. In addition, both proposed methods for estimating its mean squared error seem adequate.