Model Assisted Estimation of a Spatial Population Mean

This paper deals with the estimation of the mean of a finite spatial population defined on a fine grid superimposed over a continuous domain. Under a designbased perspective, an estimator assisted by low-rank spline smoothers of the population data is proposed and studied. Proof is given that the estimator is design-consistent and has a normal limiting distribution. A simulation study is conducted to investigate the performance of the new estimator and of the estimator of its variance, in terms of relative bias, efficiency and confidence interval coverage rate.