Non-parametric small area estimation using penalized spline regression

Opsomer JD, Claeskens G, Ranalli MG, Kauermann G, Breidt FJ (2008)
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 70(1): 265-286.

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Abstract
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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Opsomer JD, Claeskens G, Ranalli MG, Kauermann G, Breidt FJ. Non-parametric small area estimation using penalized spline regression. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY. 2008;70(1):265-286.
Opsomer, J. D., Claeskens, G., Ranalli, M. G., Kauermann, G., & Breidt, F. J. (2008). Non-parametric small area estimation using penalized spline regression. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 70(1), 265-286.
Opsomer, J. D., Claeskens, G., Ranalli, M. G., Kauermann, G., and Breidt, F. J. (2008). Non-parametric small area estimation using penalized spline regression. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 70, 265-286.
Opsomer, J.D., et al., 2008. Non-parametric small area estimation using penalized spline regression. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 70(1), p 265-286.
J.D. Opsomer, et al., “Non-parametric small area estimation using penalized spline regression”, JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, vol. 70, 2008, pp. 265-286.
Opsomer, J.D., Claeskens, G., Ranalli, M.G., Kauermann, G., Breidt, F.J.: Non-parametric small area estimation using penalized spline regression. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY. 70, 265-286 (2008).
Opsomer, J. D., Claeskens, G., Ranalli, M. G., Kauermann, Göran, and Breidt, F. J. “Non-parametric small area estimation using penalized spline regression”. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 70.1 (2008): 265-286.
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