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.

中文翻译：

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最近邻空间插值器及其自举均方误差估计器的基于设计的特性

从基于设计的角度来处理用于绘制区域或单元的连续人口和有限人口的最近邻空间插值，即人口是固定的，不确定性源于选择位置所采用的抽样方案。我们推导出最近邻插值器的基于设计的逐点和均匀一致性的条件。我们证明，在某些广泛应用于环境和森林调查的方案下，一致性是成立的。此外，我们提出了插值的均方根误差的伪种群自举估计量。最后，进行仿真研究以评估理论结果。