Resumen de Benchmarked estimates in small areas using linear mixed models with restrictions

María Dolores Ugarte Martínez , Ana Fernández Militino , Tomás Goicoa Mangado

• Linear mixed models have been frequently used to provide estimates in small areas. However, when aggregating small areas within the same region, the sum of these small area estimates does not generally match up with the estimate obtained using an appropriate estimator for the larger region. Then, benchmarking the model-dependent estimates to the ones obtained at certain level of aggregation is needed. In this paper, we propose a small area estimator based on a linear mixed effects model with restrictions to guarantee the concordance between the aggregations of small area estimates and those reported by statistical agencies for larger domains using a synthetic estimator. The mean squared prediction error of the restricted estimator is also derived and its performance is evaluated through a simulation study. The procedure is applied to the 2002 Business Survey of the Basque Country, Spain.