Small area estimation under unit-level generalized additive models for location, scale and shape

Small Area Estimation (SAE) models commonly assume Normal distribution or, more generally, exponential family. We propose a SAE unit-level model based on Generalized Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS completely release the exponential family distributional assumption and allow each parameter to depend on covariates. Besides, a bootstrap approach to estimate MSE is proposed. The performance of the estimators is evaluated with model- and design-based simulations. Results show that the proposed predictor works better than the well-known EBLUP. The SAE model based on GAMLSS is used to estimate the per-capita expenditure in small areas, based on the Italian data.