Nonparametric Small Area Estimation Using Penalized Spline Regression

18 Pages Posted: 12 Jan 2006

See all articles by J. D. Opsomer

J. D. Opsomer

Iowa State University

Gerda Claeskens

KU Leuven - Department of Economics

M. Giovanna Ranalli

University of Perugia

Göran Kauermann

Technische Universität Berlin (TU Berlin)

F. J. Breidt

Colorado State University

Date Written: January 10, 2005

Abstract

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.

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

Suggested Citation

Opsomer, J. D. and Claeskens, Gerda and Ranalli, M. Giovanna and Kauermann, Göran and Breidt, F. J., Nonparametric Small Area Estimation Using Penalized Spline Regression (January 10, 2005). Available at SSRN: https://ssrn.com/abstract=875321 or http://dx.doi.org/10.2139/ssrn.875321

J. D. Opsomer (Contact Author)

Iowa State University ( email )

613 Wallace Road
Ames, IA 50011
United States

Gerda Claeskens

KU Leuven - Department of Economics ( email )

Leuven, B-3000
Belgium

M. Giovanna Ranalli

University of Perugia ( email )

Via Pascoli 22
Perugia
Italy

Göran Kauermann

Technische Universität Berlin (TU Berlin) ( email )

Straße des 17
Berlin, 10623
Germany

F. J. Breidt

Colorado State University ( email )

Fort Collins, CO 80523
United States

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