Optimal sampling designs for nonparametric estimation of spatial averages of random fields

International audienceOptimal designs of sampling spatial locations in estimating spatial averages of randomfields are considered. The random field is assumed to have correlated values according to acovariance function. The quality of estimation is measured by the mean squared error. Simplenonparametric linear estimators along with sampling designs having a limiting densityare considered. For a large class of locally isotropic random fields, we argue for the asymptoticoptimality of simple linear estimators. The convergent rates of the mean squared errorand optimal limiting densities of sampling designs are determined in every dimension. Anexample of simulation is given