Statistical Modelling 12(6) (2012), 527–549
Small area semiparametric additive monotone models
C. Rueda
IMUVA
Instituto de Matemáticas
University of Valladolid
Spain
email: crueda@eio.uva.es
MJ. Lombardía
Dpto Matemáticas
University of Coruña
Spain
Abstract:
In this paper, semiparametric monotone mixed models are introduced, exploring, in particular, the problems of estimation and bootstrapping. The models are de?ned in a small area setting, using the assumption that some of the auxiliary variables have a monotone relationship with the response, and with the incorporation of linear terms to model other auxiliaries as the dummy variables. An estimator for the variance of the random effects is proposed and two bootstrap approaches, specially designed for monotone regression, are given to estimate the mean squared error for the area means. A simulation experiment is carried out to compare the performance of the new model-based estimators against the Fay-Herriot approach and to confirm the good performance of the bootstrap. The semiparametric model-based area estimators are also compared with the parametric-based estimators using data on a survey of lakes, where the questions of the prediction of missing data and model selection are nicely solved using simple proposals.
Keywords:
isotonic models; mixed models; monotone models; order restricted inferences; small area estimation
Downloads:
Data from Opsomer et al. (2008). For code, please contact the authors.
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