Non-parametric small area estimation using penalized spline regression

• 成果类型: Article
• 署名作者: Opsomer, J. D.; Claeskens, G.; Ranalli, M. G.; Kauermann, G.; Breidt, F. J.
• 署名单位: Colorado State University System; Colorado State University Fort Collins; KU Leuven; University of Perugia; University of Bielefeld
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2007.00635.x
• 发表日期: 2008
• 页码: 265-286
• 关键词: likelihood ratio tests; mean squared error; uncertainty; prediction; models

摘要

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.