A Test Of Hypothesis Concerning A Proposed Model For The Underlying Variogram - Introduction

The variogram is the function used to express the intercorrelation of a regionalized variable. It is used to quantify, for example, the natural variability of mineralization and in that sense may be thought of a average disimilarity between metal quantity at two points inside a deposit.2 As David2 explains, appropriate mathematical functions of distance and direction are used to characterize variograms, a process that he says is analogous to selecting a normal or lognormal model for an observed distribution. Methods for choosing a model for the underlying variogram of a random function based on the sample data appear in the literature.3,8 A crossvalidation procedure is available to check the validity of the model.3 However, statistical validation of the choice of the model through the mechanism of hypothesis testing is not presently available. In the section to follow, notation and background material is presented upon which a large sample test procedure will be constructed. The stationarity assumptions presented refer to covariance stationarity. A test procedure is then proposed, and an example is given for the case of the one dimensional random process.