Novas contribuições para avaliação e descrição da estrutura de dependência espacial em geoestatística

Abstract

This thesis aimed at developing a study on aspects of evaluation and description of spatial dependence structure in geostatistical data. First, a correction is proposed, in the exponential and gaussian models, based on the explanation percentage of the contribution parameter. In order to allow a description of the degree of spatial dependence, the construction of three indexes was proposed from the concept of spatial dependence area of the semivariogram. Second, a comparative study between the indexes was done. For the evaluation of spatial dependence, two hypothesis tests were constructed; the first with a simulation, the second by permutation. Subsequently, a study on the nominal level and the power of the two tests was done. The correlation performed on the exponential and gaussian semivariogram models allowed the generation of a new class of exponential and gaussian models. Three new indexes were formulated for the description of the spatial dependence, denominated IDE1, IDE2 and IDE3. In carrying out a comparative application of the three indexes, it was observed, in a general way, that the IDE3 index presented a better performance. Regarding the evaluation of the spatial dependence structure, two tests were constructed, denominated TDE1 and TDE2, independent of each other, for the hypothesis of the existence of spatial independence. Both tests presented similar results in relation to Type I and Type II errors and to the power. It is concluded that the IDE3 index is the best and, therefore, its use is suggested for the description of spatial dependence. In addition, both hypothesis tests, for evaluating spatial dependence, presented similar performance, which suggests the use of either one.