A Monte Carlo integration approach to Horvitz-Thompson estimation in replicated environmental designs

In environmental protocols some replicates of the selected design are usually considered in order to estimate the target parameter. Subsequently, the Horvitz- Thompson (HT) estimator is computed for each design replicate and the overall estimator arises from the average of the single estimators. Since the target parameter may be expressed as a suitable integral of the HT estimator function, in the present paper the duality of Monte Carlo (MC) integration strategies and replicated-design procedures is shown.