Addressing Covariate Lack in Unit-Level Small Area Models Using GAMLSS

The primary goal of this study is to estimate the Theil index using a unit-level Small Area Estimation (SAE) model. This has lead two primary challenges in the unit-level SAE field: the identification of individual covariates and the reduction of computational burden. We propose a unit-level Simplified SAE model based on Generalized Additive Models for Location, Scale and Shape (GAMLSS), which is specified without covariates and is able to reduce variability in comparison with the direct estimator. The performance of the proposed model used to estimate the Theil index is evaluated based on design-based simulations. An application to the Italian Regions, distinguish between Urban, Peri-Urban and Rural areas, conclude the paper.