Doctor of Philosophy

dissertationThe semivariogram is a function characterizing the second-order dependence structure of an intrinsically stationary random field; its estimation has applications in spatial statistics, particularly in the construction of optimal predictors of the random field at unobserved locations. In this work, we establish conditions under which the empirical isotropic semivariogram converges to the semivariogram uniformly on compact sets. In preparation for these results, we also establish sufficient conditions for stationary Gaussian random fields to be -mixing, in terms of the spectral density. We also introduce two new applications of semivariogram estimation: a method for digital image compression, and a refinement of the Moran's I test for spatial autocorrelation