Pseudo-population bootstrap for design-based inference on spatial populations

This paper explores variance or mean squared error estimation in the design-based inferential framework, focusing on a broad class of estimators and sampling schemes commonly employed in spatial surveys for both continuous populations and finite populations of areas. Specifically, the use of the pseudo-population bootstrap is proposed. It involves constructing a spatial pseudo-population from the sample data using the inverse distance weighting interpolator and then selecting bootstrap samples from the pseudo-population using the same sampling scheme adopted to select the original sample. The properties of the resulting variance or mean squared error estimators are theoretically investigated and empirically assessed through a simulation study. Two case studies are considered.