Geographic Information in Small Area Estimation: Small Area Models and Spatially Correlated Random Area Effects

This work applies the Fay-Herriot model in which spatial information is introduced as auxiliary variables, and generalizes the model by introducing spatially correlated random area effects modelled through the Simultaneously Autoregressive (SAR) process. The traditional Empirical Best Linear Unbiased Predictor (EBLUP) takes advantage of the between small area-variation. The evidence is that the EBLUP estimator is significantly better than the sample-size dependent estimators, especially when the between small area-variation is not large relative to the within small area variation. This suggests that the location of the small areas may also be relevant in modelling the small area parameters and that further improvement in the EBLUP estimator can be gained by including eventual spatial interaction among random area effects. The properties of the proposed estimators are evaluated by applying them to two agro- environmental case studies.