Small area estimation under spatial nonstationarity

In this paper a geographical weighted pseudo empirical best linear unbiased predictor (GWEBLUP) for small area averages is proposed, and two approaches for estimating its mean squared error (MSE), a conditional approach and an unconditional one, are developed. The popular empirical best linear unbiased predictor (EBLUP) under the linear mixed model and its associated MSE estimator are obtained as a special case of the GWEBLUP. Empirical results using both model-based and design-based simulations, with the latter based on two real data sets, show that the GWEBLUP predictor can lead to efficiency gains when spatial nonstationarity is present in the data. A practical gain from using the GWEBLUP is in small area estimation for out of sample areas. In this case the efficient use of geographical information can potentially improve upon conventional synthetic estimation.