Beyond normality: small area estimation based on generalized additive models for location, scale, and shape.

This research presents three papers that explore new methodologies at the intersection of Small Area Estimation (SAE) and Generalized Additive Models for Location, Scale, and Shape (GAMLSS), contributing novel insights to socioeconomic statistics. The first proposal introduces a SAE model based on GAMLSS, SAE-GAMLSS, for estimating household indicators. This model challenges traditional assumptions of normality by allowing more than 100 different distributions (Rigby et al., 2019). In GAMLSS each parameter can depend on covariates. Simulation results demonstrate that SAE-GAMLSS outperforms the empirical best linear unbiased predictor in various scenarios. In the application, per-capita consumption at the regional level is estimated, distinguishing between urban and rural areas, and reveals nuanced findings regarding the North-South economic divide for foreigners in Italy. The second study focuses on economic inequality among foreigners in Italy at the regional level, distinguishing between urban, peri-urban, and rural areas. A Simplified SAE-GAMLSS is proposed to overcome two common challenges in unit-level SAE: difficulties in finding covariates and high computational times. The Simplified SAE-GAMLSS, even without covariates, effectively reduces the variability of the direct estimator, minimizing computational burden. Simulation results support these findings. In the application, the Atkinson index is estimated. Findings indicate significant disparities in inequality between foreigners and natives, providing valuable insights for formulating targeted policies promoting equity and immigrant integration. Lastly, the third investigation addresses the critical issue of measuring the Carbon Footprint (CFP) at the household level. The study proposes the use of a conversion factor matrix to bridge macroeconomic data with consumption data and suggests employing the Generalized Beta Distribution of the Second kind (GB2) to describe households’ CFP. To obtain reliable per-capita CFP estimates at the provincial level, a SAE-GAMLSS based on a GB2 distribution is introduced.