Small area estimation using skew normal models

Two connected extensions of the Fay–Herriot small area level model that are of practical and theoretical interest are proposed. The first extension allows for the sampling error to be non-symmetrically distributed. This is important for cases in which the sample sizes in the areas are not large enough to rely on the central limit theorem (CLT). This is dealt with by assuming that the sample error is skew normally distributed. The second extension proposes to jointly model the direct survey estimator and its respective variance estimator, borrowing strength from all areas. In this way, all sources of uncertainties are taken into account. The proposed model has been applied to a real data set and compared with the usual Fay–Herriot model under the assumption of unknown sampling variances. A simulation study was carried out to evaluate the frequentist properties of the proposed model. The evaluation studies show that the proposed model is more efficient for small area predictions under skewed data than the customarily employed normal area model. ► Two extensions of the Fay–Herriot small area level model are proposed. ► The first one allows for the sampling error to be non-symmetrically distributed. ► The second one proposes to jointly model the direct survey estimator and its variance. ► The evaluation studies show that our proposed model is superior to the normal model.