General Linear Models in Small Area Estimation: An Assessment in Agricultural Surveys

In recent years one of the most difficult problem to solve by the official statistical institutes is the information delivery about small geographical areas. In the context of agriculture, there is a growing demand for reliable small area statistics in order to assess or to put into effect agricultural policies and programs. Data collected form some well-organized sample surveys, like the farm structure surveys, can be used only to derive direct estimates for large areas, such as administrative districts or regions of national territories. Sample sizes in small domains of interest are typically reduced by the survey design itself, if the objective is to provide accurate estimates at higher level of aggregation than that of small areas. In any case, direct estimates in specific areas are not reliable, because the smallness of sample sizes in the areas can drive to unacceptably large standard errors. One of the most recurrent method of small area estimation is based on models that consider composite estimates (Ghosh and Rao, 1994). This models combine synthetic and direct estimates, balancing the potential bias of the synthetic estimates with the instability of the direct estimates by a weighted average of the two functions. Some models (Ghosh and Rao, 1994; Rao, 2002) such as EBLUP (empirical best linear unbiased prediction), involve design-based and model-based random variables, and analyze random area effects through the use of area level and unit level mixed linear statistical models (Robinson, 1991). Th