Small area estimation with spatial similarity

We derive a class of composite estimators of small-area quantities that exploit spatial (distance-related) similarity. They are based on a distribution-free model for the areas, but the estimators are aimed to have optimal design-based properties. Composition is applied also to estimating some of the global parameters on which the small-area estimators depend. We show that the commonly adopted assumption of random effects is not necessary for exploiting the similarity of the districts (borrowing strength across the districts). The methods are applied to estimation of the mean household sizes and the proportions of single-member households in the counties (comarcas) of Catalonia. Key phrases: Auxiliary information, composite estimation, design-based estimator, exploiting similarity, model-based estimator, multivariate shrinkage, small-area estimation, spatial similarity. JEL Classification: C1 (Econometric and Statistical Methods): C13 — Estimation; C14 — Semiparametric and nonparametric methods; C15 — Simulation methods. C4 (Special Topics): C42 — Survey methods. Address for correspondence: N. T. Longford, Departament d’Economia i Empresa, Universitat Pompeu Fabra, Ramon Trias Fargas 25–27, 08005 Barcelona, Spain. Email: [email protected] .