Constrained optimal neighborhoods and kernel estimators as improvements to applications of kriging.

Abstract

The motivation for this dissertation is to develop innovations in spatial, environmental data analyses, using kriging and kernel estimation, that form a basis for an eventual automation of the calculations. Special consideration should be given to the different requirements for environmental data as compared to the mining data generally used in the evaluation of kriging applications. It is common to use standard search neighborhoods in the applications of kriging. It is one object of this dissertation to develop variable search neighborhoods and to extend the use of these search neighborhoods to experimental variogram calculations. Other objectives include incorporating one dimensional kernel estimation into variogram calculation; and augmenting kriging with two and three dimensional kernel estimators. These three different areas require the development of programs to accomplish the following: (1) Generate elliptical neighborhoods with variable parameters in two dimensions and ellipsoidal neighborhoods with variable parameters in three dimensions; and calculate experimental variograms using these neighborhoods to limit the number of data pairs used and thereby reduce the effects of drift. (2) Calculate experimental variograms with a one dimensional kernel to separate the bin width from the number of points which is not possible with the standard experimental variogram. (3) Use two or three dimensional kernel estimators to provide an alternate to kriging.