Small area estimation using skew normal models

Valmária Rocha da Silva ∗ Fernando Antônio da Silva Moura † Abstract The main aim of this work is to propose two important connected extensions of the Fay and Heriot (1979) area level small area estimation model that might be of practical and theoretical interests. The first extension allows for the sampling error to be non-symmetrically distributed. This is important for the case that the sample sizes in the areas are not large enough to rely on the Central Limit Theorem. We deal with this by assuming that the sample error is skew-normal distributed. The second extension proposes to jointly model the direct survey estimator and its respective variance estimator. Proceeding in this way, we manage to take into account all sources of uncertainties. We applied our proposed model to a real data set and compare with the usual Fay-Heriot model under the assumptions of the unknown sampling variance. We also carried out a simulation study to evaluate frequentist properties of our proposed model. As it expected, our evaluation studies show that our proposed model are more efficient for producing small are prediction under skew data.