Design‐based properties of the nearest neighbor spatial interpolator and its bootstrap mean squared error estimator
Lorenzo Fattorini, Marzia Marcheselli, Caterina Pisani, Luca Pratelli · Biometrics · 2021
Nearest neighbor spatial interpolation for mapping continuous populations and finite populations of areas or units is approached from a design-based perspective, that is, populations are fixed, and uncertainty stems from the sampling scheme adopted to select locations. We derive conditions for design-based pointwise and uniform consistency of the nearest neighbor interpolators. We prove that consistency holds under certain schemes that are widely applied in environmental and forest surveys. Furthermore, we propose a pseudopopulation bootstrap estimator of the root mean squared errors of the interpolated values. Finally, a simulation study is performed to assess the theoretical results.