Riemann Estimation for Replicated Environmental Sampling Designs

In many environmental surveys the population under study is made up of biological units scattered over a planar region. A variable is considered on each unit and the target parameter generally turns out to be the population total of the variable. In order to estimate the population total, field scientists commonly replicate a suitable design on the study region. Replicated environmental designs basically rely on the selection of a set of sample points, in such a way that each sample point corresponds to a single design replicate. Frequently, the sample points are located uniformly and independently over the planar region, even if more effective strategies are actually available. The population total is subsequently estimated by using the mean of the estimates obtained in each design replicate. However, this pooled estimator may be improved by considering a suitable weighted mean - rather than the simple mean - of the estimates. Thus, we propose a Riemann estimator of the population total which is actually borrowed from the Monte Carlo integration setting. The suggested estimator displays appealing performance from both theoretical and practical perspectives.