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

Abstract: We propose a Small Area Estimation model based on Generalized Additive Models for Location, Scale and Shape (SAE-GAMLSS), for the estimation of household economic indicators. SAE-GAMLSS release the exponential family distributional assumption and allow each distributional parameter to depend on covariates. A bootstrap approach to estimate MSE is proposed. The SAE-GAMLSS estimator shows a largely better performance than the well-known EBLUP, under various simulated scenarios. Based on SAE-GAMLSS per-capita consumption of Italian and foreign households in Italian regions, in urban and rural areas, is estimated. Results show that the well-known Italian North-South divide does not hold for foreigners.