Nonparametric small area estimation using penalized spline regression
Opsomer, Jean × Claeskens, Gerda Ranalli, Maria Giovanna Kauermann, Goeran Breidt, F #
Royal Statistical Society
Journal of the Royal Statistical Society. Series B, Statistical methodology vol:70 pages:265-286
This article proposes a 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 nonparametric small area estimation problem as a mixed effect model regression. The resulting model is readily fitted using existing model fitting approaches such as restricted maximum likelihood. We present theoretical results on the prediction mean squared error of the proposed estimator and on likelihood ratio tests for random effects, and we propose a simple nonparametric 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.