Finite population properties of predictors based on spatial patterns

When statistical inference is used for spatial prediction, the model-based framework known as kriging is commonly used. The predictor for an unsampled element of a population is a weighted combination of sampled values, in which weights are obtained by estimating the spatial covariance function. This solution can be affected by model misspecification and can be influenced by sampling design properties. In classical design-based finite population inference, these problems can be overcome; nevertheless, spatial solutions are still seldom used for this purpose. Through the efficient use of spatial information, a conceptual framework for design-based estimation has been developed in this study. We propose a standardized weighted predictor for unsampled spatial data, using the population information regarding spatial locations directly in the weighting system. Our procedure does not require model estimation of the spatial pattern because the spatial relationship is captured exclusively based on the Euclidean distances between locations (which are fixed and do not require assessment after sample selection). The individual predictor is a design-based ratio estimator, and we illustrate its properties for simple random sampling.