Nonparametric Small Area Estimation Using Penalized Spline Regression

We propose a new small area estimation approach that combines small area random effects with a smooth, nonparametrically specified trend. By using penalized splines as the representation for the nonparametric trend, it is possible to express the small area estimation problem as a mixed effect model regression. This model is readily fitted using existing model fitting approaches such as restricted maximum likelihood. We develop a corresponding bootstrap approach for model inference and estimation of the small area prediction mean squared error. The applicability of the method is demonstrated on a survey of lakes in the Northeastern US