Semiparametric Fay-Herriot model using Penalized Splines

In this paper we propose a semiparametric Fay and Herriot area level model based on P­splines, which can handle situations where the functional form of the relationship between the variable of interest and the covariates is unknown. This is often the case when the data are supposed to be affected by spatial proximity effects. In these cases P­spline bivariate smoothing can easily introduce spatial effects in the area level model. By this spatial effect we can obtain estimates for out of sample areas and also for those areas where auxiliary information is unavailable. We focus here on the small area mean estimator and on an analytic and a bootstrap based mean squared error estimators. The proposed estimators of the small area means and mean squared errors are contrasted to the traditional ones by means of two simulations studies. We finally present results of the application of our semiparametric model to estimate the mean of the Acid Binding Capacity (ANC) and Calcium (CA) concentration in streams for each 8­digit Hydrologic Unit Code (HUC) within the Mid­Atlantic region of the US. ANC and CA concentration represent two of the key indicators to keep under control for environmental protection and preservation of natural resources. These results present evidence that the proposed estimators can be used to obtain accurate estimates in those areas where direct estimates are unreliable or even unavailable.