Monte Carlo integration strategies for design-based regression estimators of the spatial mean

When a continuous population is sampled, the spatial mean is often the target parameter if the design-based approach is assumed. In this case, auxiliary information may be suitably used to increase the accuracy of the spatial mean estimators. To this end, regression models are usually considered at the estimation stage in order to implement regression estimators. Since the spatial mean may be obviously represented as a bivariate integral, the strategies for placing the sampling locations are actually Monte Carlo integration methods. Hence, the regression-based estimation is equivalent to the control-variate integration method. In this setting, we suggest more refined Monte Carlo integration strategies which may drastically increase the regression estimator accuracy. Copyright (c) 2005 John Wiley & Sons, Ltd.