Estimation and Prediction in the Presence of Spatial Confounding for Spatial Linear Models
研究了空间模型中协变量与误差相关时系数估计和空间预测的性质，发现广义最小二乘估计有偏但预测误差可能降低，对空间数据分析者有用。
Abstract In studies that produce data with spatial structure, it is common that covariates of interest vary spatially in addition to the error. Because of this, the error and covariate are often correlated. When this occurs, it is difficult to distinguish the covariate effect from residual spatial variation. In an i.i.d. normal error setting, it is well known that this type of correlation produces biased coefficient estimates, but predictions remain unbiased. In a spatial setting, recent studies have shown that coefficient estimates remain biased, but spatial prediction has not been addressed. The purpose of this paper is to provide a more detailed study of coefficient estimation from spatial models when covariate and error are correlated and then begin a formal study regarding spatial prediction. This is carried out by investigating properties of the generalized least squares estimator and the best linear unbiased predictor when a spatial random effect and a covariate are jointly modelled. Under this setup, we demonstrate that the mean squared prediction error is possibly reduced when covariate and error are correlated.