Small area estimation under a spatially non-linear model

We describe a methodology for small area estimation of counts that assumes an area level version of a nonparametric generalized linear mixed model with a mean structure defined using spatial splines. The proposed method represents an alternative to other small area estimation methods based on area level spatial models that are designed for both spatially stationary and spatially non-stationary populations. We develop an estimator for the mean squared error of the proposed small area predictor as well as an approach for testing for the presence of spatial structure in the data and evaluate both the proposed small area predictor and its mean squared error estimator via simulations studies. Our empirical results show that when data are spatially non-stationary the proposed small area predictor outperforms other area level estimators in common use and that the proposed mean squared error estimator tracks the actual mean squared error reasonably well, with confidence intervals based on it achieving close to nominal coverage. An application to poverty estimation using household consumer expenditure survey data from 2011–12 collected by the national sample survey office of India is presented.