Out of Sample Estimation for Small Areas using Area Level Data
Out of Sample Estimation for Small Areas using Area Level Data
A Fay-Herriot type model with independent area effects is often assumed when small area estimates based on area level data are required. However, under this approach out of sample areas are limited to synthetic estimates. In this paper we relax the independent area effects assumption, allowing area random effects to be spatially correlated. Empirical best linear unbiased predictors are then developed for areas in sample as well as those that are not in sample, with variance components estimated via maximum likelihood and residual (restricted) maximum likelihood. An expression for the mean cross-product error (MCPE) matrix of the small area estimators is derived, as is an estimator of this matrix. The estimation approach described in the paper is then evaluated by a simulation study, which compares the new method with other methods of small area estimation for this situation.
Spatial correlation, Random effects, Maximum likelihood, REML, Simultaneous autoregressive model.
Southampton Statistical Sciences Research Institute, University of Southampton
Saei, Ayoub
d9202095-5650-4b3d-9b13-a8d16e10b338
Chambers, Ray
96331700-f45e-4483-a887-fef921888ff2
10 February 2005
Saei, Ayoub
d9202095-5650-4b3d-9b13-a8d16e10b338
Chambers, Ray
96331700-f45e-4483-a887-fef921888ff2
Saei, Ayoub and Chambers, Ray
(2005)
Out of Sample Estimation for Small Areas using Area Level Data
(S3RI Methodology Working Papers, M05/11)
Southampton, UK.
Southampton Statistical Sciences Research Institute, University of Southampton
23pp.
Record type:
Monograph
(Working Paper)
Abstract
A Fay-Herriot type model with independent area effects is often assumed when small area estimates based on area level data are required. However, under this approach out of sample areas are limited to synthetic estimates. In this paper we relax the independent area effects assumption, allowing area random effects to be spatially correlated. Empirical best linear unbiased predictors are then developed for areas in sample as well as those that are not in sample, with variance components estimated via maximum likelihood and residual (restricted) maximum likelihood. An expression for the mean cross-product error (MCPE) matrix of the small area estimators is derived, as is an estimator of this matrix. The estimation approach described in the paper is then evaluated by a simulation study, which compares the new method with other methods of small area estimation for this situation.
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Published date: 10 February 2005
Keywords:
Spatial correlation, Random effects, Maximum likelihood, REML, Simultaneous autoregressive model.
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Local EPrints ID: 14327
URI: http://eprints.soton.ac.uk/id/eprint/14327
PURE UUID: 67576179-30a1-4c97-9cec-c1f35876cf21
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Date deposited: 10 Feb 2005
Last modified: 20 Feb 2024 03:20
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Author:
Ayoub Saei
Author:
Ray Chambers
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