Design-based Consistent Strategies Exploiting Auxiliary Information in Environmental Mapping

Abstract 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 ( k NN) 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 k NN 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 k NN 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.