Spatial estimation: the geostatistical point of view

Geostatistics involves the statistical estimation of erratic surfaces, similar to those found in geology, using sample data. It has been my experience that there are few texts in geostatistics written for people who are new to the subject, and who have not been immersed in it since its inception in the 1960's. To prevent other people becoming confused by the changing notation, and unspoken assumptions, I provide an overview of this subject, with the aim of providing a clearer understanding of the concepts involved, the assumptions made, and the motivation behind each type of estimator. I then concentrate on the more general form of estimation assuming a nonhomogeneous trend, called Universal Kriging. I explain in detail how this estimator can be found in an accurate and computationally efficient way. Using the information gained from robustness studies of this estimator, I then attempt to apply it to real surfaces, for different methods of covariance estimation and trend orders.Science, Faculty ofMathematics, Department ofGraduat