A BLUP Synthetic Versus an EBLUP Estimator: An Empirical Study of a Small Area Estimation Problem

Model-based estimators are becoming very popular in statistical offices because Governments require accurate estimates for small domains that were not planned when the study was designed, as their inclusion would have produced an increase in the cost of the study. The sample sizes in these domains are very small or even zero; consequently, traditional direct design-based estimators lead to unacceptably large standard errors. In this regard, model-based estimators that ‘borrow information’ from related areas by using auxiliary information are appropriate. This paper reviews, under the model-based approach, a BLUP synthetic and an EBLUP estimator. The goal is to obtain estimators of domain totals when there are several domains with very small sample sizes or without sampled units. We also provide detailed expressions of the mean squared error at different levels of aggregation. The results are illustrated with real data from the Basque Country Business Survey.