Non-parametric small area estimation using penalized spline regression

Authors: Opsomer, J. D.¹; Claeskens, G.²; Ranalli, M. G.³; Kauermann, G.⁴; Breidt, F. J.¹

Source: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 70, Number 1, February 2008 , pp. 265-286(22)

Publisher: Wiley-Blackwell

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Abstract:

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.

Keywords: Best linear unbiased prediction; Bootstrap inference; Mixed model; Natural resource survey

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2007.00635.x

Affiliations: 1: Colorado State University, Fort Collins, USA 2: Katholieke Universiteit Leuven, Belgium 3: Università degli Studi di Perugia, Italy 4: Universität Bielefeld, Germany

Publication date: 2008-02-01