A Small Area Predictor under Area-Level Linear Mixed Models with Restrictions

Abstract

A calibrated small area predictor based on an area-level linear mixed model with restrictions is proposed. It is showed that such restricted predictor, which guarantees the concordance between the small area estimates and a known estimate at the aggregate level, is the best linear unbiased predictor. The mean squared prediction error of the calibrated predictor is discussed. Further, a restricted predictor under a particular time-series and cross-sectional model is presented. Within a simulation study based on real data collected from a longitudinal survey conducted by a national statistical office, the proposed estimator is compared with other competitive restricted and non-restricted predictors.

Keywords:

• Best linear unbiased prediction
• Calibrated predictor
• Linear mixed model
• Mean squared prediction error of the calibrated predictor
• Small area estimation

2000 Mathematics Subject Classification:

• 62D05
• 62F40
• 62J99

Acknowledgments

We thank the anonymous referee for a number of constructive comments which have considerably improved an earlier version of the article. We are grateful to the Associate Editor for useful suggestions which led to significant improvement in the presentation of this article. Thanks also for the Portuguese statistical office for the availability of the data used in the research. The views expressed here are solely those of the authors. Finally we are grateful to Fundaçãopara a Cincia e a Tecnologia (Portugal) for financial support.

Notes

The CV for the direct estimator is estimated from the design-based perspective, i.e., using the sampling design; the CV for the synthetic estimator is estimated from the model based perspective, i.e., considering model uncertainty.

Results in this table refer to model-based CVs. For the RY predictor CVs are estimated using the RY analytical method; for the calibrated predictors CVs are estimated using the proposed bootstrap parametric method.