Hierarquização geométrica dos preditores geoestatísticos

Abstract

Geostatistics estimation is a probabilistic modeling strategy that uses sample points neighborhood information in order to consider the spatial dependence of the structure of a STOCHASTICprocess to obtain, unbiased and minimum variance estimates. Hence, the main goal of this thesis is to present the geometric hierarchy of the geostatistical linear predictors, taking into account their restrictions and respective projection subspaces. We apply the orthogonal geometric projection of the predictors in order to obtain a vector function Y(x0), (that represents a value to be predicted in the location (x0)) in the resulting vector subspace from the restrictions imposed to the predictors. As an important result obtained in our work, we show how to obtain geometric hierarchy: Conditional expectation, simple linear kriging and linear universal kriging, 1st, 2nd and 3rd, respectively. We establish practical conditions for using such predictors, and we ilustrate our findings with stochastic simulations.