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Non‐parametric small area estimation using penalized spline regression
Author(s) -
Opsomer J. D.,
Claeskens G.,
Ranalli M. G.,
Kauermann G.,
Breidt F. J.
Publication year - 2008
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00635.x
Subject(s) - small area estimation , estimator , parametric statistics , spline (mechanical) , statistics , mean squared error , mathematics , parametric model , estimation , inference , regression , regression analysis , restricted maximum likelihood , estimation theory , computer science , artificial intelligence , engineering , structural engineering , systems engineering
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.