Abstract

Assessing and monitoring natural resources and biodiversity is a burning issue and totals of interest attributes, as well as suitable function of totals, usually constitute parameters to be estimated. Moreover, detailed information about the spatial pattern of natural resources is essential and mapping is required for a visual overview. In design-based inference spatial populations are constituted by fixed sets of locations in a study region with fixed values of the survey variable attached to each location. Populations can be distinguished into continuous populations, finite populations of areal units partitioning the study region or finite populations of units. In the case of populations of units, the list is rarely available, and units are commonly sampled using points selected on the study region. Owing to the presence of positive spatial autocorrelation and of spatial heterogeneity, schemes which ensure the selection of points or areal units “well spread” onto the study region should be adopted. Well spread samples can be straightforwardly obtained by means of tessellation sampling schemes: tessellation stratified sampling and systematic grid sampling for continuous populations, one-per-stratum stratified sampling and systematic sampling for finite populations of areal units.
The asymptotic framework and the conditions ensuring design-based consistency of the Horvitz-Thompson total estimator and of the inverse distance weighting interpolator adopted for mapping are summarized for both continuous and finite populations of areal units .