Variogram model selection via nonparametric derivative estimation

Before optimal linear prediction can be performed on spatial data sets, the variogram is usually estimated at various lags and a parametric model is f itted to those estimates. Apart from possible a priori knowledge about the process and the user's subjectivity, there is no standard methodology for c hoosing among valid variogram models like the spherical or the exponential ones. This paper discusses the nonparametric estimation of the variogram an d its derivative, based on the spectral representation of positive definite functions. The use of the estimated derivative to help choose among valid parametric variogram models is presented. Once a model is selected, its par ameters can be estimated-for example, by generalized least squares. A small simulation study is performed that demonstrates the usefulness of estimati ng the derivative to help model selection and illustrates the issue of alia sing.