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 distribution assumption and allow each parameter to depend on covariates. Besides, a bootstrap approach to estimate MSE is proposed. The performance of the proposed estimators is evaluated with model- and design-based simulations. Results show that the proposed redictor work better than the well-known EBLUP. The presented models are used to estimate the per-capita expenditure in small areas, based on the Italian data.

翻译：小域估计（SAE）模型通常假定正态分布，或更一般地，属于指数族分布。本文提出一种基于位置、尺度与形状广义可加模型（GAMLSS）的单位级SAE模型。GAMLSS完全放宽了指数族分布假设，并允许每个参数依赖于协变量。此外，本文提出一种估计均方误差（MSE）的自助法。通过基于模型和基于设计的模拟评估所提出估计量的性能。结果表明，所提出的预测器优于知名的EBLUP。本文提出的模型用于基于意大利数据估计小区域的人均支出。