The estimation of a surface throughout a continuum of points in a study area is addressed by means of two-phase sampling strategies. To this aim, a family of two-phase inverse distance weighting interpolators is introduced, and their design-based asymptotic properties are derived when the surface remains fixed and the number of sample points approaches infinity. In particular, conditions ensuring asymptotic unbiasedness and consistency are derived and are proven to hold for some of the most widely applied environmental sampling schemes. Furthermore, a computationally simple mean squared error estimator is proposed. Finally, a simulation study is performed to assess the theoretical results. The proposed strategy is adopted to provide the map of basal area in a forested region of Casentino Valley (Central Italy).
The authors wish to thank Piermaria Corona, Director of the Forestry Research Centre, for stimulating this research and providing many suggestions and data, and Nicola Puletti from Forestry Research Centre for his assistance in the case study.
"Two-phase sampling strategies for design-based mapping of continuous spatial populations in environmental surveys." Ann. Appl. Stat. 15 (1) 287 - 303, March 2021. https://doi.org/10.1214/20-AOAS1392