Sampling and kriging spatial means: efficiency and conditions

Sampling and estimation of geographical attributes that vary across space (e.g., area temperature, urban pollution level, provincial cultivated land, regional population mortality and state agricultural production) are common yet important constituents of many real-world applications. Spatial attribute estimation and the associated accuracy depend on the available sampling design and statistical inference modelling. In the present work, our concern is areal attribute estimation, in which the spatial sampling and Kriging means are compared in terms of mean values, variances of mean values, comparative efficiencies and underlying conditions. Both the theoretical analysis and the empirical study show that the mean Kriging technique outperforms other commonly-used techniques. Estimation techniques that account for spatial correlation (dependence) are more efficient than those that do not, whereas the comparative efficiencies of the various methods change with surface features. The mean Kriging technique can be applied to other spatially distributed attributes, as well.