Including Spatial Information in Estimation from Complex Survey Data

This chapter focuses on the estimation phase of a survey. We assume that we have data coming from a possibly complex sampling design and that we are interested in doing inference for a set of descriptive parameters of a finite population. We focus on estimation of finite population totals and (differentiable) functions thereof. We consider a design-based framework for inference, that is, the population values of the variables of interest are considered as fixed quantities, so that randomness comes into play only from the sampling design. Since we are interested in accounting for the spatial structure that very likely characterizes agricultural and environmental populations, we also consider superpopulation models in our inferential framework. These models assist our estimation procedures in the hope of providing more accurate estimates. However, we only consider design-consistent estimators that are robust to model misspecifications: these estimators show an improved efficiency if the model well describes the population values of the variable of interest, but they are not biased in the case of model failure. Therefore, we consider a model-assisted approach to inference in the sense of Särndal et al. (1992) and not a model-based approach.