Non‐parametric small area estimation using penalized spline regression

Summary.  The paper proposes a small area estimation approach that combines small area random effects with a smooth, non‐parametrically specified trend. By using penalized splines as the representation for the non‐parametric trend, it is possible to express the non‐parametric small area estimation problem as a mixed effect model regression. The resulting model is readily fitted by using existing model fitting approaches such as restricted maximum likelihood. We present theoretical results on the prediction mean‐squared error of the estimator proposed and on likelihood ratio tests for random effects, and we propose a simple non‐parametric 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 north‐eastern USA.

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