Viewing a non stochastic spatial interpolator under a design based probabilistic framework

When inference regards a finite spatial pattern, a model-based framework is commonly used, even if the problem of model misspecification may occur. In classical design-based inference, this problem is overcome; nevertheless spatial solutions in this direction are still under development. Through an efficient use of spatial information a design based conceptual framework for estimation is carried out: we propose a ratio type estimator for spatial data, where the information on spatial locations of the population is used. In spatial prediction the usual second order inclusion probabilities are not the most useful tool: rather, the probabilities of association between sampled and unsampled individuals are the core of the proposed design-based estimator.