  Two-stage hierarchical models have been widely used in small area estimation
to produce indirect estimates of areal means. When the areas are treated
exchangeably and the model parameters are assumed to be the same over all
areas, we might lose the efficiency in the presence of spatial heterogeneity.
To overcome this problem, we consider a two-stage area-level model based on
natural exponential family with spatially varying model parameters. We employ
geographically weighted regression approach to estimating the varying
parameters and suggest a new empirical Bayes estimator of the areal mean. We
also discuss some related problems, including the mean squared error
estimation, benchmarked estimation, and estimation in non-sampled areas. The
performance of the proposed method is evaluated through simulations and
applications to two data sets.
