Statistical Modelling 10 (2010), 215–239
Small area estimation under Fay–Herriot models with non-parametric
estimation of heteroscedasticity
Wenceslao González-Manteiga
Departamento de Estadística e Investigación Operativa
Facultad de Matemáticas
Universidad de Santiago de Compostela
Campus Sur
E–15706 Santiago de Compostela
Spain
eMail: wenceslao.gonzalez@usc.es
MJ Lombarda
Departamento de Matemáticas
Universidade da Coruña
Spain
I Molina
Departamento de Estadística
Universidad Carlos III de Madrid
Spain
D Morales and L Santamaría
Centro de Investigación Operativa
Universidad Miguel Hernández de Elche
Spain
Abstract:
Fay–Herriot models relate direct estimators of small area means to vectors
of area-level auxiliary covariates. Estimation of error variances in these
models is a problem because of the lack of data within areas. A non-parametric
approach is proposed for estimating these variances. Estimators of the
remaining model parameters are derived and their asymptotic properties are
studied. Moreover, small area estimators that incorporate the estimated error
variances are obtained and several simple estimators of the mean squared error
of these estimators are proposed. Simulation experiments study the small
sample performance of the new small area estimators and compare the different
estimators of the mean squared errors. Finally, the results are applied to the
estimation of unemployment proportions in Spanish domains.
Keywords:
bandwidth parameter; bootstrap; kernel estimation; linear mixed model;
small area estimation
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