Stability analysis in nonstationary spatial covariance estimation

Space deformation modelling and estimation techniques based on Multidimensional Scaling (MDS) methods play an important role in nonparametric approaches to the covariance structure analysis of the spatiotemporal processes underlying environmental studies. Since any related procedure depends on the planar MDS representation, the stability of the estimated dispersion, together with the determination of the most influential stations in the estimation of the dispersion space, are important issues that must be analysed before performing the final mapping. In this paper, stability analysis, both in terms of the MDS model and of the variogram function, as well as concerning the derivation of kriging interpolation estimates, is addressed using a special analytical jackknife procedure. Furthermore, the influence of each station in the solution given is assessed, thus providing relevant information regarding not only the MDS procedure but also the interpolation process and the variogram estimation of the spatial dispersion.