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

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.