Design-based Consistent Strategies Exploiting Auxiliary Information in Environmental Mapping

Mapping continuous populations and finite populations of areas is approached in a design-based framework. The Tobler’s law is adopted as assisting model, suggesting the use of inverse distance weighting (IDW) and k nearest neighbor (kNN) interpolators. The two interpolators are also able to exploit information provided by the huge list of inexpensive auxiliary data deriving from remote sensing sources. Conditions ensuring design-based consistency of kNN and IDW interpolators exploiting auxiliary information are derived under very simple tessellated schemes widely applied in environmental surveys. Simulation studies performed on a real population fully confirm the theoretical findings. Consistency results about kNN can be extended to random forest imputation techniques, that in the last years have been increasingly applied in mapping forest and environmental resources. Supplementary materials accompanying this paper appear online.