Small area estimation for skewed semicontinuous spatially structured responses

When surveys are not originally designed to produce estimates for small geographical areas, some of these domains can be poorly represented in the sample. In such cases, model-based small area estimators can be used to improve the accuracy of the estimates by borrowing information from other sub-populations. Frequently, in surveys related to agriculture, forestry or the environment, we are interested in analyzing continuous variables which are characterized by a strong spatial structure, a skewed distribution and a point mass on zero. In such cases standard methods for small area estimation, which are based on linear mixed models, can be inefficient. The aim of this chapter is to discuss small area estimation models suggested in literature to handle zero-inflated, skewed, spatially structured data and to present them under the unified approach of generalized two-part random effects models.