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.

翻译：小域估计（SAE）模型通常假设正态分布或更一般的指数族分布。本文提出了一种基于位置、尺度和形状广义可加模型（GAMLSS）的SAE单位级模型。GAMLSS完全释放了指数族分布假设，并允许每个参数依赖于协变量。此外，本文还提出了一种用于估计均方误差（MSE）的自助法。通过基于模型和基于设计的模拟评估了估计量的性能。结果表明，所提出的预测器优于著名的EBLUP。基于GAMLSS的SAE模型被用于基于意大利数据估计小域的人均支出。