On the Design of Experiments Under Spatial Correlation
研究误差空间相关时实验设计的影响，发现普通最小二乘下A有效设计对相关结构不敏感，而广义最小二乘下效率排序稳定但长程与短程相关有重要差异。
The implications for experimental design when the errors are spatially correlated are investigated. The first part of the paper considers the case when treatment effects are estimated by ordinary least-squares. If only treatment labels are randomized, then A-efficient designs are reasonably independent of the correlation structure, but this is not so for other efficiency criteria. If randomization of designs is considered within one of the classical design sets, then restricted randomizations may be chosen to reduce the variations in efficiency. The distributions of the usual sums of squares are also discussed. The second part considers the case when the analysis to be used is generalized least-squares using a known correlation matrix. Then for a particular correlation structure the efficiency orderings are relatively stable over different criteria, but there are important differences between long-range and short-range correlations whatever the criterion. The efficiency gain over ordinary least-squares is shown to be least for long-range structures. Predictions made from theoretical results on the torus (Martin, 1982) are shown to have some validity in the plane. In both parts numerical evaluations provide illustrations.